Papers

In this work, we characterize the glassy character of the Bose-glass phase in a disordered Bose-Hubbard model using three complementary diagnostics: the finite-temperature spectral function, spatial inhomogeneity, and the inverse participation ratio. Spectral analysis, obtained from finite-temperature Green's function and random phase approximation, shows that disorder introduces localized low-energy states within the Mott gap, eventually closing the gap at sufficiently strong disorder. Spatial inhomogeneity, calculated using the Gutzwiller ansatz, increases sharply with disorder and then saturates at moderate disorder strengths. The inverse participation ratio has been calculated from the exact diagonalization of a small system, and it reveals enhanced localization with stronger disorder. Increasing temperature suppresses these disorder-induced features: the low-energy spectral weight diminishes, the spatial inhomogeneity varies more smoothly, and the IPR decreases. Taken together, these diagnostics show that disorder drives the development of glassy character, while thermal fluctuations gradually wash out its signatures. The early saturation of spatial inhomogeneity compared with the continued evolution of low-energy excitations and the inverse participation ratio demonstrates that no single diagnostic fully captures the evolution of the Bose-glass state, highlighting the need for a combined characterization.

Universal power-law decay of spin-mixing oscillations has been observed in a harmonically trapped spin-$3/2$ Fermi gas, whose exactly equally spaced spectrum represents a highly special case. To gain insight into the origin of this behavior, we investigate the dynamics in traps with increasing and decreasing level spacings, represented by the infinite square well and the Pöschl–Teller potential, respectively. Despite pronounced differences in their single-particle spectra, all systems exhibit power-law decay of coherent oscillations, described by $A(t) = A_{0} - \gamma t^{\alpha}$. The exponent $\alpha$ remains insensitive to particle number, interaction strength, and the overall energy scale, but exhibits systematic differences among traps with distinct spectral structures. In contrast, the decay parameter $\gamma$ is strongly influenced by both the spectral structure and the overall energy scale. These findings demonstrate that power-law decay is not restricted to the harmonic trap but persists across qualitatively distinct spectral structures. The observed variation of $\alpha$ among different traps further suggests that the underlying single-particle spectrum plays an important role in shaping the decay dynamics.

We derive exact finite-size nonperturbative representations of equilibrium modal occupations and related statistics for three representative nonlinear systems: the Majda-McLaughlin-Tabak dispersive-wave model, the Fermi-Pasta-Ulam-Tsingou beta anharmonic chain, and the discrete nonlinear Schrodinger lattice field. Independent simulations confirm the predictions from weak to strong nonlinearity. For DNLS, the theory remains accurate across the weak-coupling quasicondensation crossover, where large low-mode occupations and long-range coherence amplify interaction effects even when the bare nonlinear coefficient is small. The finite-ring DNLS occupations are further resolved into a positive sum of Rayleigh-Jeans channels with distinct correlation lengths, explaining when a single Rayleigh-Jeans law applies and why it fails near quasicondensation. In MMT and DNLS, the exact occupations also determine the mean modal frequencies even when the dynamical spectra broaden or split. The nonperturbative results allow a direct assessment of two representative perturbative approaches. Treating the mean interaction appropriately yields accurate low-order approximations, including at strong nonlinearity. At higher orders, however, the corrections cease to decrease and successive approximations oscillate with increasing amplitude; both finite-order approaches also fail near weak-coupling quasicondensation. Thus neither low-order agreement nor a small bare coupling guarantees a reliable perturbative description. The results establish nonperturbative equilibrium theory for widely used nonlinear wave and lattice models and provide a quantitative basis for modal distributions of energy, particles, and optical power in nonlinear optics, dispersive waves, anharmonic lattices, and cold-atom systems.

Whether a full counting statistical distribution preserves its universality class across a coherent-to-incoherent crossover is a fundamental question in open quantum systems. We resolve this for the infinite-$U$ Hubbard chain, showing that local density dephasing changes transport exponents without destroying the underlying non-Gaussian M-Wright spin fluctuations. Utilizing the exact spin-charge composition law inherent to impenetrable dynamics, we track the charge sector from ballistic flow to diffusive hydrodynamics. This dissipative crossover shifts the characteristic spin-transfer width from $t^{1/4}$ to $t^{1/8}$. Despite this altered scaling time, the central spin characteristic functions uniformly collapse onto a singular M-Wright scaling function, what we confirm using analytics as well as numerics.

We introduce a self-adaptive Floquet system based on a quantum kicked rotor, in which the kicking strength itself becomes a dynamical variable generated self-consistently through cavity-mediated feedback. A superradiant transition gives rise to cavity-mediated kicking and two competing instability channels, symmetric and antisymmetric, which provide a unified organizing principle for the nonequilibrium Floquet phases. For resonant kicking, their competition produces double-kick dynamics that support resonant ballistic transport and an emergent antiresonance with period-quadrupled rotor evolution, arising from a balance between the two instability channels. Remarkably, for incommensurate kicking, the antisymmetric instability stabilizes a robust period-doubled localized phase with persistent subharmonic dynamics despite the underlying incommensurate driving, revealing localized temporal order absent in conventional kicked rotors. As the feedback strength increases, correlated temporal fluctuations progressively suppress quantum interference, driving crossovers from period-doubled localization to irregular localization and eventually to subdiffusive transport. Our results establish a general framework for self-adaptive quantum-chaotic dynamics and demonstrate how dynamical feedback can fundamentally reshape transport, localization, and temporal order in driven quantum systems.

We investigate the dynamics of gap solitons found in the Harper-Hofstadter model with an additional cubic nonlinearity, such as that describing weakly-interacting cold atoms or a Kerr nonlinearity in an optical platform. We find that certain solitons with frequencies deep in the band gap travel with a robust, quantized velocity perpendicular to the applied force and maintain their spatial profile over long timescales. Crucially, this velocity is linearly proportional to the applied force, allowing for arbitrary steering of the nonlinear wavepacket, without breakdown, using only a tunable external force. This quantized transport persists despite a highly non-uniform occupation of the linear Bloch states, and contrasts with solitons near the band edge, which deform and delocalize under the same force. These results point to a robust and highly controllable mechanism for steering nonlinear solitons in experimentally accessible platforms.

Matrix product operator (MPO) serves as a fundamental component in tensor network simulations of quantum many-body dynamics. We employ an MPO construction that introduces additional propagation channels to embed both periodic boundary conditions and finite-range couplings directly into an open boundary MPO. We apply this construction within the time-dependent variational principle (TDVP) framework to simulate quench dynamics in a spin-1/2 chain with finite-range interactions, and benchmark the results numerically against the fourth-order Runge-Kutta method, finding excellent agreement for both single-body and two-body observables. The approach offers a practical route for tensor network simulations of many-body dynamics in periodic finite-range systems.

We investigate the nonequilibrium evolution of density correlations in a thermal one-dimensional Bose gas following a trap quench. We focus on the Tonks–Girardeau limit and develop an analytical description based on a finite-temperature extension of Quantum Generalized Hydrodynamics. We benchmark our predictions against exact numerics for a quench from a double well to a harmonic trap and for a trap release, and assess their temperature range of validity. Our results capture the dynamical enhancement of correlations during the expansion stages, namely the crossover from thermally suppressed to power-law bulk correlations. For the trap release, the conformal distance associated with fixed bulk points decreases as $1/t$, so the correlations progressively probe a universal regime~$\sim1/x^2$ that is independent of temperature. We thus show that, in the hydrodynamic long-time regime, the bulk density correlations approach their zero-temperature equilibrium form independently of the initial temperature.

Distinguishing altermagnetism from conventional ferromagnetism and antiferromagnetism typically relies on momentum-space probes. Here, we show that the real-space spreading of a localized spin excitation provides a distinctive dynamical fingerprint of altermagnetic order. Using linear spin-wave theory on a two-dimensional checkerboard lattice with nearest-neighbor and next-nearest-neighbor couplings J_1 and J_2, we demonstrate that finite J_2 produces direction-dependent magnon group velocities and splits the two magnon branches. The resulting propagation remains closer to that of an antiferromagnet than a ferromagnet, retaining an approximately circular outer wavefront, while the direction-dependent magnon velocities produce a pronounced cross-like spatial structure inside this front. We further show that changing the sign of J_2 to enter the unfrustrated regime (J_2<0) increases the characteristic propagation velocities and interchanges the diagonal directions of enhanced propagation, corresponding to a pi/2 rotation of the anisotropic spatial pattern. These results establish spacetime dynamics as a complementary probe of altermagnetic magnons, providing a route to identifying unconventional magnetic order through real-space propagation patterns in solid-state and synthetic quantum systems.

Two-component supersolids can exhibit in-phase or out-of-phase component density modulations, corresponding to density and spin supersolids, respectively. We formulate a general hydrodynamic theory for the collective dynamics of multicomponent supersolids, guided by their broken symmetries and conservation laws. We benchmark it against microscopic calculations for a binary dipolar condensate confined to an infinite tube, finding quantitative agreement for the sound speeds of all three Goldstone branches throughout the density- and spin-supersolid regions. The resulting relations link collective-mode measurements to elastic coefficients and superfluid fractions.

We study a Fermi-Hubbard model coupled to a open dissipative single cavity mode. Using Keldysh diagrammatics we derive and solve the quantum kinetic equations for the fermions, taking the bosonic cavity mode as a source of non-equilibrium noise and dissipation. In absence of Hubbard interactions we show that the fermions reach generically a non-equilibrium steady-state, characterized by a non-thermal distribution function. Quite interestingly we demonstrate that the latter exactly nullifies the heat-current between fermions and cavity mode. We discuss the regimes of parameters where a low-frequency effective temperature description emerges and how the fluctuations affect the mean-field phase diagram for the superradiance phase transition. Finally we include Hubbard interaction in the weak-coupling regime and show that it leads to a crossover towards a full equilibrium distribution.

In order to understand which initial states retain memory under periodic driving, it is necessary to depart from the ideal limit giving rise to invariant structures and work inside near-degenerate manifolds. We show that degeneracy itself is not conclusive and what actually matters is how perturbations, such as structural and driving imperfections, acts on the projected multiplet. For systems decoupling into the local clusters in the ideal limit, the projections can be computed within degenerate perturbation theory. There the stability is decided by two criteria: the coupling can not connect the state with other degenerate partners in the manifold, either by kinetic blocking, or more generally, by diagonalizing the projected coupling, and the drive's local selection rule must admit only transfer energies detuned from Floquet sidebands, in which case the projected drive generator exactly vanishes. We formalize these understandings in a periodically driven clean, short-ranged alternating XXZ chain and demonstrate a set of results that include, long-lived states, both of product form and entangled across the clusters, a periodic family of sideband resonances, and an explicit example showing opposite fates for states with identical energy and charges.

Many-body localization is remarkable in that localization persists despite the presence of dynamical interactions. Here we demonstrate the converse phenomenon: enhanced many-body delocalization induced solely by exchange statistics. We study a Aubry-André quasiperiodic system of anyons in one dimension in the absence of density-density interactions. In terms of anyon operators, the system is described by a quadratic Hamiltonian. By analyzing the finite-size scaling of its spectral properties and the inverse participation ratio of many-body eigenstates, we find that increasing the anyonic statistical phase systematically shifts the many-body localization crossover toward larger quasiperdiodic potentials. We further confirm these findings using a dynamical probe, namely the persistence of an initial density imbalance following quenches. Our results establish exchange statistics as an independent mechanism capable of altering many-body localization, revealing a fundamentally distinct route to delocalization in one-dimensional quantum systems.

In this article, we study the dipolar Bosonic quantum fluid. The fluid experiences mean-field, beyond mean-field, and three body interactions. We investigate their competition with dipolar interaction and fragmentation as a result of this competition. We further investigate the elementary excitations and note two distinct dispersion regimes, namely roton-mode and modulational instability. We support our observation by calculating the superfluid fraction and the condensate fraction.

The area law relates the bipartite entanglement entropy of a quantum many-body ground state to the size of the boundary between the subsystems, but the geometry of this boundary is rarely discussed. We inspect this in the 1D Bose-Hubbard model at fixed density by comparing four spatial bipartitions of the periodic lattice: first half, second half, even sites, and odd sites; sharing the same number of sites but differing in how the boundary is arranged. We find analytical limits with perturbation theory: in the Mott insulator the contiguous cut obeys the area lay while the alternating cut obeys a volume law $S\propto N_s$, in this sense an anomaly, and for the superfluid both cuts colapse to the binomial saturation due to delocalization of the state. We formulate these limits as a statement about the many-body problem using a generalized slave-boson approach based on mean-field with quantum fluctuations while verifying with Exact Diagonalization (ED) for small lattice sizes and Densitiy Matrix Renormalization Group (DMRG) simulations for $N_s\gg 1$. The slave-boson Gaussian ground state allows to compute the entanglement entropy from a reduced correlation matrix for any desired bipartition consistent with ED and DMRG results. Using slave bosons the computational cost is set by the local cutoff $n_{\max}$ rather than the Hilbert space dimension, so we can reach lattice sizes far beyond ED. Our method is capable of establishing the partition-dependent scaling laws as a many-body feature, not only a finite-size effect, in great agreement with the ED for $N_s\in[4,10]$ and DMRG for larger lattice sizes.

The controlled dynamical generation of radial dam break flows (DBFs) is demonstrated in two-dimensional droplet environments. These ultracold mixtures feature competing mean-field and quantum fluctuation effects and are initialized on a disk-shaped uniform density. Depending on the value of the latter, reflecting also the dominance of attractive or repulsive interactions, three dynamical response regimes are identified. At small densities a moving wavetrain of bright ring solitons is observed (dubbed ring DBF), at intermediate densities a ring kink-dispersive shock wave, while at large densities the flows encompass composite ring kink-rarefaction waves moving towards the center. The emergence of these patterns, whose formation would be prohibited in two-dimensional Kerr media due to wave-collapse, is rooted in the competition between attraction and repulsion inherent to droplet environments, modeled by the extended Gross-Pitaevskii equation. The characterization of the ensuing nonlinear waveforms is further corroborated by reduced models based on the cubic-quintic nonlinear Schrödinger equation. The different wave patterns emanating from dam break flows can be experimentally realized using current state-of-the-art ultracold atom experiments.

Bad metals exhibit approximately $T$-linear dc resistivity beyond the Ioffe–Regel limit. That this behavior occurs in systems with radically different ground states suggests it is a generic manifestation of strong local correlations. We test this hypothesis in the infinite-$U$ Hubbard model with small hole densities using exact diagonalization to compute thermodynamic and transport properties of finite clusters. Upon cooling, we find an intermediate temperature range, an electronic analogue of the “semi-quantum regime” of liquid helium, in which quantum effects produce a roughly $T$-independent compressibility, yet the resistivity is $T$-linear and exceeds the Ioffe–Regel limit. Entry into this regime is accompanied by the formation of quasi-local ferromagnetic “spin cages” around doped holes, regions that facilitate local quantum motion embedded in a fluctuating spin background, analogous to the transient crystalline cages thought to control incoherent transport in semi-quantum liquid helium. Remarkably, despite the simplicity of the model, the bad metal behavior found here resembles that seen in various material platforms.

Hysteresis and retrapping are hallmarks of underdamped Josephson dynamics, yet they have remained elusive in atomic Josephson junctions. Here, we introduce a velocity-sweep protocol to demonstrate these phenomena in the underdamped regime of an atomic Josephson junction. Specifically, using classical-field simulations of a two-dimensional bosonic superfluid, we show hysteresis in the velocity-imbalance characteristics and determine the retrapping current. The dynamics are quantitatively captured by the resistively and capacitively shunted junction (RCSJ) model. We show that hysteresis originates from persistent phase slips below the critical current, with the associated dissipation mediated by vortex-antivortex pair nucleation at the weak link. The retrapping current follows the Stewart-McCumber scaling of underdamped junctions, establishing a common phase-dynamical framework for atomic and superconducting Josephson junctions.

Recent quantum gas cavity-QED experiments demonstrated simultaneous coupling of photons to single atom transitions as well as correlated pairs of ultracold fermions trapped inside optical cavities. This enables simultaneous control over density ordering and pairing. Using extensive numerical simulations, we show that in a transversely driven, two-component degenerate Fermi gas, the interplay of cavity-induced and bare atom–atom interactions controls not only the power threshold for self-organization, but also the type of spatial ordering in the $\mathbb Z_2$-symmetry-broken superradiant state. In the repulsive interaction regime, unpaired or weakly paired fermions first self-organize through a charge-density-wave instability, and finite-momentum pairing only occurs at much stronger pump strengths. In contrast, an attractive superfluid undergoes a joint density–pairing instability, directly entering into intertwined phase with charge-density-wave and pair-density-wave orders. At strong pumping the photon-enhanced pair interaction generates localized density and pairing order even when the bare contact interaction is repulsive. In this cavity-dominated regime strong spatial localization suppresses the long range superfluid coherence. Our results identify the role of cavity-induced atomic interactions in supporting intertwined fermionic orders and pave the way for exploring exotic states with multiple orders in highly controlled hybrid light-matter systems.

We investigate the ground-state properties of a two-component attractive Fermi gas confined to a spherical surface, demonstrating how curvature and finite-size effects lead to qualitatively different behavior compared to the planar limit. In the strongly attractive regime, the system forms a Bose-Einstein condensate (BEC) of tightly bound dimers, yielding a gap and chemical potential that approach flat-space results with leading-order geometric corrections. However, as the attraction decreases, the system crosses over into a Bardeen-Cooper-Schrieffer (BCS) regime where the Cooper pair size becomes constrained by the sphere radius, producing pronounced deviations from flat-space behavior. We identify strong shell effects at magic particle numbers set by the single-particle spectrum, revealing the geometry-driven suppression of fermionic pairing at weak interactions. Our results highlight a fundamental interplay among geometry, quantum statistics, and interactions, motivating future experiments with shell-trapped ultracold fermions and inspiring geometry-controlled condensed matter devices.

This course on two-dimensional quantum gases, prepared for the São Paulo ICTP-SAIFR IVth School on Light and Cold Atoms, is organized into three lectures. The first introductory lecture addresses Bose-Einstein condensation in an ideal gas, the effect of interactions in the weakly interacting limit, Gross-Pitaevskii equation and its hydrodynamic formulation, as well as superfluidity. The second lecture is devoted to the main features of two-dimensional quantum gases: importance of the interactions, enhanced phase fluctuations and the emergence of a quasi long-range order, superfluidity through the Berezinskii-Kosterlitz-Thouless mechanism, scaling symmetry. The third lecture has taken the form of a seminar on fast rotating quasi two-dimensional Bose gases and thermal melting of the vortex lattice. The slides accompanying these notes can be found on the school website: https://www.ictp-saifr.org/slca2025/.

We address three-dimensional (3D) solitons maintained by spin-orbit coupling (SOC) in the binary self-interacting Bose-Einstein condensate (BEC) held in the 3D optical lattice (OL). The analysis reveals that the SOC-OL interplay results in the formation of stable full-vortex (FV) soli-tons, built as sets of four density peaks residing in neighboring wells of the lattice potential, with the superimposed global vortical phase, and site-centered semi-vortices (SV), in which the vorticity is present in only one component. The full-vortex solitons, with their specific phase textures, do not exist in a uniform BEC with SOC. Full-vortex and semi-vortex states in the binary self-attractive BEC are stable despite the possibility of the supercritical collapse in the 3D system. Such states also exist, as gap solitons, in the self-repulsive 3D system. In terms of the chemical potential and number of particles, the stability regions of the 3D full-vortex solitons and semi-vortices expand with the increase of the SOC strength and OL depth. The results open the route to the creation of 3D complexes of vorticity-carrying condensates that can be realized with existing experimental techniques.

Motivated by recent experimental realizations of the Heisenberg model and two-dimensional altermagnetism using ultracold atoms in optical lattices, we systematically investigate the magnetic properties of the square-lattice Heisenberg $J_1$-$J_2$-$J_2^\prime$ model in the presence of easy-axis single-ion anisotropy $D$. Here, $J_1 (>0)$ is the nearest-neighbor antiferromagnetic exchange parameter, while $J_2$ and $J_2^\prime$ are two distinct next-nearest-neighbor superexchange parameters that alternate on the lattice. We perform numerical calculations of the sublattice magnetization, net magnetization, and critical temperature. Interestingly, the net magnetization is not identically zero at finite temperatures; its absolute value first increases and then decreases with increasing temperature, revealing a temperature-dependent weak ferromagnetism. We find that $J_2\not=J_2^\prime$ is the primary factor responsible for weak ferromagnetism at finite temperatures, while $D$ provides the necessary background for two-dimensional long-range magnetic ordering. Moreover, for a fixed $J_2+J_2^\prime$, we observe that a larger $|J_2-J_2^\prime|$ leads to a greater maximum net magnetization and critical temperature, as well as a broader temperature range for weak ferromagnetism. The difference between $J_2$ and $J_2^\prime$ originates from the distinct superexchange pathways between magnetic atoms, with these pathways mediated by two different types of nonmagnetic atoms. This mechanism, which differs from conventional ones such as the Dzyaloshinskii-Moriya interaction, may be detectable in real materials.

We show that an $O(1)$ local defect is sufficient to generate approximate unitary $k$-designs from an otherwise integrable quantum many-body system. Using a two-Pauli-kick (2PK) protocol with temporal sampling, we demonstrate this mechanism in a fixed-magnetization sector of deterministic XXZ spin chains with a single integrability-breaking bulk defect. We derive an analytical selection rule for the Pauli kicks and show that symmetry-preserving strings with a specific domain-wall count, fixed by the couplings, govern design formation. An exhaustive search over all admissible Pauli strings identifies a broad family of kicks that produce designs in the chaotic regime, whereas no such kicks exist in the integrable limit, including for boundary defects. We further show that the design-forming mechanism remains effective for weak bulk defects as the system size increases.

The characteristic feature of counterflow superfluids consisting of $N\geq 3$ components – the so-called Borromean supercounterfluids (BSCF) – is the presence of $N$ distinct elementary topological excitations (vortices) despite having only $N-1$ independent Goldstone modes. We show that this remarkable property clearly manifests itself at the Berezinskii-Kosterlitz-Thouless-type transition from the BSCF to the normal state, under the conditions of slight to moderate deviations from the case of exact intercomponent symmetry. More generally, our analysis also applies to any multicomponent superfluid with intercomponent drag fine-tuned to the value when certain composite vortices compete energetically with elementary ones.

We propose a variational shortcut-to-adiabaticity scheme for the fast dynamical control of one-dimensional quantum droplets in ultracold Bose-Bose mixtures. The control is implemented through time-dependent mean-field (MF) and beyond-mean-field (BMF) nonlinearities, which can be adjusted by tuning intra- and interspecies scattering lengths near Feshbach resonances. Using a bright-droplet variational ansatz, together with inverse engineering, we derive time-dependent interaction protocols that connect prescribed initial and target self-bound states while suppressing residual excitations. We analyze three representative settings: simultaneous control of the MF and BMF terms, control with fixed BMF nonlinearity and time-dependent MF interaction, and control with fixed MF nonlinearity and time-dependent BMF interaction. For the constrained cases, additional variational degrees of freedom are introduced to optimize the protocols while respecting the imposed restrictions. Direct numerical simulations of the extended Gross-Pitaevskii equation confirm final fidelities exceeding $0.99$ on short time scales, and show that the optimised protocols are robust against finite calibration errors of the nonlinear control strength. Our results provide a route toward fast state-to-state manipulation of self-bound quantum fluids and may be useful for controlled matter-wave engineering in ultracold mixtures.

We study a two-dimensional paired Fermi system in which altermagnetism produces a spin splitting that depends on momentum. The interaction strength is described through the two-body binding energy, so that the chemical potential and pairing gap evolve self-consistently from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime to the strong-coupling Bose-Einstein-condensate (BEC) regime at fixed density. The stability of the uniform paired state is examined by giving the pairs a small center-of-mass momentum and following the resulting change in free energy. We show that at zero temperature, the phase stiffness follows a universal quadratic suppression, $J/J_0 = 1 - (\alpha/\alpha_0)^2$, across the entire fully gapped crossover regime. Deviations from this relation emerge only on the BCS side upon the opening of gapless Bogoliubov pockets, which rapidly reduce the stiffness and can trigger an instability toward finite-momentum pairing. In the BEC regime, this universal quadratic correction corresponds to the altered effective mass of the tightly bound composite bosons. The model therefore provides a simple setting in which to compare altermagnetic pair breaking on the BCS and BEC sides of the crossover.

We investigate local conserved quantities in non-Hermitian bosonic lattice systems whose underlying Yang–Baxter structure remains unclear. Focusing on a one-dimensional bosonic chain with quartic interactions of creation operators, we provide a new representation of the local conserved quantities previously constructed by Sanatani and Shiraishi. Using Fourier transformation and trigonometric identities, we systematically derive these conserved quantities and show directly that they form a mutually commuting family. We further extend the construction to interactions extending beyond a single site, cubic interactions, asymmetric hopping, and an on-site potential. Our results provide a unified framework for constructing and characterizing local conserved quantities in this class of non-Hermitian many-body systems.

The Scharnhorst effect in quantum electrodynamics predicts a superluminal velocity shift $\delta c>0$ at low photon frequencies due to vacuum fluctuations between two mirrors. Although theoretically robust (no causality violation), the effect is extraordinarily small ($\delta c/c\approx 10^{-32}$ for mirrors $1\,\mu{\rm m}$ apart) and outside current experimental reach. Here we propose a condensed matter analogue, replacing the photons in the electromagnetic vacuum by phonon excitations of a Bose-Einstein condensate. In an idealized geometry, the two-dimensional surface of a cylinder (circumference $L$) at zero temperature, the axial speed of sound is increased due to zero-point fluctuations of the condensate by $\delta c/c\simeq 5\times 10^{-3}\,\tilde{g}$ at $L\simeq 2\,\xi$, to first order in the dimensionless interaction constant $\tilde{g}\simeq 10^{-1}$ of the Bose gas of healing length $\xi\simeq 1\,\mu{\rm m}$. This is 28 orders of magnitude larger than the photonic effect, basically because phonons have a self-interaction while photons only interact via massive electrons. We discuss the prospects for observation of the acoustic Scharnhorst effect, the main restriction being the low-temperature requirement.

We develop a surrogate-assisted workflow for millimeter-scale transport of a $^{87}$Rb Bose–Einstein condensate (BEC) on a multi-wire atom chip. Gradient-based inverse optimization generates 42 current schedules spanning seven regularization strengths and six transport durations. A low-cost Gaussian phase-space model ranks these schedules by endpoint overlap at three atom numbers. A Thomas–Fermi scaling (Ermakov) model estimates cloud dimensions for case-specific moving-grid construction. We then evaluate selected schedules in detail with the three-dimensional Gross–Pitaevskii equation (GPE). At $N=10^3$ and $T=0.5$ s, the surrogate predicts a larger axial center-of-mass (COM) excursion than at longer durations. The GPE confirms this prediction and reveals sloshing that persists through delivery, with an endpoint fidelity $F_{3D}=0.9244$. For all five longer transports, the surrogate predicts near-unit endpoint overlap for the top-ranked schedules, and GPE propagation using these schedules gives $F_{3D}>0.9997$. At $N=10^4$ and $T=2.0$ s, the surrogate-selected schedule similarly gives $F_{3D}=0.999932$. These results demonstrate that the surrogate estimates provide a useful low-cost basis for candidate screening, while GPE propagation resolves the transport dynamics and the delivered condensate state.