arXiv subjects

Thomas Gasenzer

Publications and source records attributed to Thomas Gasenzer.

At least 19 recordsLinked to original sources

arXiv2026

Jones-Roberts solitary waves and the onset of rotation in a spherical surface condensate

The nonlinear excitations underlying the onset of rotation in a dilute Bose-Einstein condensate confined to a thin spherical shell are studied. These excitations correspond to solitary waves rotating about the sphere at constant angular speed: at low speeds they appear as dipoles of singly quantized vortices with opposite circulation, while at higher speeds they evolve into vortex-free Jones-Roberts solitons. With further increase of the angular speed, these excitations hybridize with equatorially confined modes whose azimuthal wave number is set by the sphere radius measured in units of the healing length. The propagation speed of these modes is shown to play the role of a Landau critical velocity, thereby setting the upper limiting angular speed of the entire Jones-Roberts family.

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arXiv2026

Observation of sine-Gordon-like solitons in a spinor Bose-Einstein condensate

We experimentally generate sine-Gordon-like solitons in a spin-1 spinor Bose-Einstein condensate (BEC) utilizing a robust and reproducible local phase-imprinting scheme. We find that the soliton velocity can be tuned by the effective quadratic Zeeman shift. This enables the investigation of controlled soliton interactions, in which we observe the characteristic elastic collision behavior of the integrable sine-Gordon model. The spatial displacement -- the so-called phase shift -- between incoming and outgoing solitons, the signature of their pairwise interaction, is found to be in quantitative agreement with numerical spin-1 simulations within the error bars. These results establish spinor BECs as a highly controllable experimental platform for studying aspects of the dynamics of sine-Gordon-like models.

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arXiv2026

Quantum integrable matrix models of spinor Bose gases in one spatial dimension

Degenerate spinor Bose gases with repulsive density-density interaction and anti-ferromagnetic spin-spin coupling in one spatial dimension are shown to be described by a quantum integrable matrix extension of the nonlinear Schr\"odinger model, whose fundamental fields are described by an $m\,\times\,n$ matrix of bosonic field operators. The eigenstates of this model are constructed for arbitrarily sized matrix field operators by means of algebraic Bethe-ansatz techniques, and the corresponding Bethe equations governing the spectra of conserved quantities are derived. The approach thus generalizes previously chosen techniques to account for arbitrary spin multiplets and their spin-spin interaction. Focusing on the specific case of the $2\times2$ model, which is shown to correspond to a spin-$1$ Bose gas, a set of integral equations is derived, which describe its equilibrium thermodynamic properties. From these, the ground state phase diagram is computed both, numerically and analytically in the parameter plane spanned by the chemical potential and an external magnetic field. Furthermore, the existence of paired bound states is shown to modify the Pauli exclusion principle for interacting bosons in one dimension. In particular, it is found that no two quasiparticle rapidities can coincide, provided that the Lieb parameter satisfies $\gamma>4/3$.

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arXiv2026

Morphological false-vacuum decay in dipolar supersolids

False-vacuum decay between two morphologically distinct supersolid phases via bubble nucleation is studied in a uniform dipolar gas confined to the plane. Starting from a metastable honeycomb state, the formation of stripe phase domains is simulated numerically by means of a stochastic projected extended Gross-Pitaevskii equation. The speed of bubble growth is analyzed in relation to the multiple speeds of sound of the supersolid, and is found to be set by the slowest of these sounds. The vacuum decay rate is numerically extracted and compared against a minimal effective model for the Coleman bounce solution connecting the two supersolid orders. Our results establish dipolar supersolids as a novel and versatile platform for studying false-vacuum decay. This setting offers a rich structure of metastable states and collective excitations that come into play in the decay. Furthermore, here, in contrast to previous studies, bubble formation occurs directly in the real-space density and can be probed with \textit{in situ} imaging.

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arXiv2025

Decaying superfluid turbulence near an anomalous non-thermal fixed point

We investigate anomalously slow coarsening in a dilute two-dimensional (2d) superfluid closed with respect to particle and energy exchange with the environment. The dynamics is demonstrated to be closely connected to both, a non-thermal fixed point (NTFP) in a far-from-equilibrium quantum system, and to Kraichnan-Kolmogorov turbulence. During a universal dynamical regime associated with an anomalous NTFP, vortex dynamics are understood to be governed by three-vortex collisions that trigger vortex-antivortex annihilation events, leading to a subdiffusive decay of the vortex density and thus growth of the characteristic inter-defect length scale, $\ell_\text{v}\sim t^{\,\beta}$ with $\beta\approx1/5$. It is found that, during the same time when this power law in time is seen, the moments of the superfluid velocity circulation $\Gamma$ around an area of spatial extent $r$ exhibit power-law scaling $\Gamma^{2}(r)\sim r^{8/3}$, in agreement with Kraichnan-Kolmogorov predictions for an inverse energy cascade in the inertial range, in a driven-open setting. Moreover, in high-order moments, intermittent deviations from linear scaling $\Gamma^{2p}(r)\sim [\Gamma^{2}(r)]^{p}$ are observed that are consistent with bifractal intermittency corrections previously measured in fully developed classical turbulence. These results establish a quantitative link between decaying quantum turbulence in a closed superfluid and universal dynamics near a non-thermal fixed point. Notably, the subdiffusive decay exponent $\beta\approx1/5$ deviates significantly from values reported for classical systems.

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arXiv2025

Anomalous non-thermal fixed point in a quasi-two-dimensional dipolar Bose gas

The emergence of distinctly sub-diffusive scaling in the vicinity of an anomalous non-thermal fixed point is discussed in a quasi-two-dimensional dipolar Bose gas in the superfluid phase, carrying ensembles of vortices and antivortices with zero net angular momentum. The observed scaling behavior reflects coarsening dynamics driven by the mutual annihilation of vortices and antivortices, with the mean inter-defect distance growing algebraically over time as $\ell_\text{v}(t)\sim t^{\,\beta}$. A sub-diffusive ($\beta<1/2$) exponent $\beta\approx0.2$ is extracted for various parameter regimes, initial conditions, and dipolar configurations from both scaling occupation-number spectra and the evolution of inter-defect distances as well as the corresponding total vortex densities. As vortex-antivortex annihilation progresses, excitations of the background condensate increase. This gives rise to a transition in the scaling behavior at late times, toward a non-thermal fixed point governed by diffusion-type scaling with $\beta\approx1/2$ as expected for the mutual annihilation of well-separated vortex-antivortex dipoles. While the temporal scaling with $\beta$ does not depend significantly on the strength and anisotropy of the dipolar interactions and thus underlines the universality of the anomalous as well as diffusion-type non-thermal fixed points, we find distinctly different vortex patterns resulting in the dipolar case. While in the superfluid with contact interactions only, same-sign vortices tend to cluster and form large-scale eddies, in the dipolar and tilted cases, roton excitations appear to prevent such motion, giving rather rise to a maximisation of distances between vortices of either sign.

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arXiv2025

Ab initio Complex Langevin computation of the roton gap for a dipolar Bose condensate

We compute from first principles the dispersion relation $\omega(k)$ of a dipolar Bose gas of erbium atoms close to the roton instability by employing the Complex Langevin (CL) algorithm. Other than the path integral Monte Carlo algorithm, which samples the quantum mechanical path integral in the $N$-particle basis, CL samples the field-theoretic path integral of interacting bosons and can be evaluated for experimentally realistic atom numbers. We extract the energy of roton excitations as a function of the s-wave scattering length, and compare our results to those from Gross-Pitaevskii theory, with and without quantum fluctuation corrections.

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arXiv2025

Kelvin waves in nonequilibrium universal dynamics of relativistic scalar field theories

We investigate the different degrees of freedom underlying far-from-equilibrium scaling behaviour in a relativistic, single-component $\mathrm{O}(1)$ scalar field theory in two and three spatial dimensions. In such a strongly correlated many-body system, identifying the respective roles of nonlinear wave excitations and defect dynamics is a prerequisite for understanding the universal character of time evolution far from equilibrium and thus the different possible universality classes of nonthermal fixed points. Using unequal-time two-point correlation functions, we extract information about the dominant infrared excitations and study their connections to the turbulent dynamics of topological defects created in the system. In three dimensions, the primary excitations are identified as kelvon quasiparticles, which are quantised Kelvin waves propagating along vortex lines, while in two dimensions, vortices are point defects, and the infrared dynamics is dominated by bound-state like excitations similar to Kelvin waves. In both cases, the kelvon excitations are found to be characterised by distinct time-evolving dispersion relations, subject to the coarsening dynamics close to the respective nonthermal fixed point and, thus, to the decay of superfluid turbulence in the system. Our results underline the role of topological defects and their influence on the universal dynamics of strongly correlated systems near nonthermal fixed points, complementing the analysis of large-$N$ models in $\mathrm{O}(N)$ systems.

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arXiv2024

Double sine-Gordon class of universal coarsening dynamics in a spin-1 Bose gas

Far from equilibrium, universal dynamics prevails in many different situations, from pattern coarsening to turbulence. A central longstanding problem concerns the development of a theory of coarsening that rests on the microscopic properties of the system and allows identifying the interaction mechanisms underlying a possible overarching universality class of the associated scaling dynamics. In quantum systems, this is complicated by the existence of nonlinear and topological excitations due to the compact nature of phase degrees of freedom. We show that the double sine-Gordon model as a noncompact low-energy effective model of the spin-1 Bose gas accounts for subdiffusive coarsening dynamics, identifying field configurations spread over multiple wells of the sinusoidal potential as a precondition for the slow scaling. This is in contrast to diffusion-type scaling which the model is known to exhibit as well, where field configurations are seen to not extend over more than two wells. Experimental observations of a spinor BEC support these characteristics, thus constituting a platform for the investigation of sine-Gordon dynamics. Our results point to a path towards a classification of pattern coarsening in many-body systems on the basis of microscopic models.

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arXiv2024

Kibble-Zurek scaling of the superfluid-supersolid transition in an elongated dipolar gas

We simulate interaction quenches crossing from a superfluid to a supersolid state in a dipolar quantum gas of ${}^{164}\mathrm{Dy}$ atoms, trapped in an elongated tube with periodic boundary conditions, via the extended Gross-Pitaevskii equation. A freeze-out time is observed through a delay in supersolid formation after crossing the critical point. We compute the density-density correlations at the freeze-out time and extract the frozen correlation length for the solid order. An analysis of the freeze-out time and correlation length versus the interaction quench rate allows us to extract universal exponents corresponding to the relaxation time and correlation length based on predictions of the Kibble-Zurek mechanism. Over several orders of magnitude, clear power-law scaling is observed for both the freeze-out time and the correlation length, and the corresponding exponents are compatible with predictions based on the excitation spectrum calculated via Bogoliubov theory. Defects due to independent local breaking of translational symmetry, contributing to globally incommensurate supersolid order, are identified, and their number at the freeze-out time is found to also scale as a power law. Our results support the hypothesis of a continuous transition whose universality class remains to be determined but appears to differ from that of the (1+1)D XY model.

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arXiv2024

Bogoliubov phonons in a Bose-Einstein condensate from the one-loop perturbative renormalization group

Wilson's renormalization-group approach to the weakly-interacting single-component Bose gas is discussed within the symmetry-broken, condensate phase. Extending upon the work by Bijlsma and Stoof [Phys. Rev. A 54, 5085 (1996), see http://doi.org/10.1103/PhysRevA.54.5085 ], wave-function renormalization of the temporal derivative contributions to the effective action is included in order to capture sound-like quasiparticle excitations with wave lengths larger than the healing-length scale. By means of a suitable rescaling scheme we achieve convergence of the coupling flows, which serve as a means to determine the condensate depletion in accordance with Bogoliubov theory, as well as the interaction-induced shift of the critical temperature.

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arXiv2023

Universal dynamics of rogue waves in a quenched spinor Bose condensate

Isolated many-body systems far from equilibrium may exhibit scaling dynamics with universal exponents indicating the proximity of the time-evolution to a non-thermal fixed point. We find universal dynamics connected with the occurrence of extreme wave excitations in the mutually coupled magnetic components of a spinor gas which propagate in an effectively random potential. The frequency of these rogue waves is affected by the time-varying spatial correlation length of the potential, giving rise to an additional exponent $δ_\mathrm{c} \simeq 1/3$ for temporal scaling, which is different from the exponent $β_V \simeq 1/4$ characterizing the scaling of the correlation length $\ell_V \sim t^{\,β_V}$ in time. As a result of the caustics, i.e., focusing events, real-time instanton defects appear in the Larmor phase of the spin-1 system as vortices in space and time. The temporal correlations governing the instanton occurrence frequency scale as $t^{\, δ_\mathrm{I}}$. This suggests that the universality class of a non-thermal fixed point could be characterized by different, mutually related exponents defining the evolution in time and space, respectively. Our results have a strong relevance for understanding pattern coarsening from first principles and potential implications for dynamics ranging from the early universe to geophysical dynamics and micro physics.

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arXiv2023

Universal Dynamics at the Lowest Temperatures

High-performance graphical processing units (GPU) are used for the repeated parallelised propagation of non-linear partial differential equations on large spatio-temporal grids. The main challenge results as a combination of the requirement of large grids for exploring scaling over several orders of magnitude, both in space and time, and the need for high statistics in averaging over many runs, in computing correlation functions for highly fluctuating quantum many-body states. With our simulations, we explore the dynamics of complex quantum systems far from equilibrium, with the aim of classifying their universal characteristics such as scaling exponents near non-thermal fixed points. Our results are strongly relevant for the development of synthetic quantum systems when exploring the respective physics in the laboratory.

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arXiv2023

Observation of two non-thermal fixed points for the same microscopic symmetry

Close to equilibrium, the underlying symmetries of a system determine its possible universal behavior. Far from equilibrium, however, different universal phenomena associated with the existence of multiple non-thermal fixed points can be realized for given microscopic symmetries. Here, we study this phenomenon using a quasi-one-dimensional spinor Bose-Einstein condensate. We prepare two different initial conditions and observe two distinct universal scaling dynamics with different exponents. Measurements of the complex-valued order parameter with spatial resolution allow us to characterize the phase-amplitude excitations for the two scenarios. Our study provides new insights into the phenomenon of universal dynamics far from equilibrium and opens a path towards mapping out the associated basins of non-thermal fixed points.

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arXiv2023

Complex Langevin approach to interacting Bose gases

Quantitative numerical analyses of interacting dilute Bose-Einstein condensates are most often based on semi-classical approximations. Since the complex-valued field-theoretic action of the Bose gas does not offer itself to the direct application of standard Monte Carlo techniques, simulations beyond their scope by now almost exclusively rely on quantum-mechanical techniques. Here we explore an alternative approach based on a Langevin-type sampling in an extended state space, known as complex Langevin (CL) algorithm. While the use of the CL technique has a long-standing history in high-energy physics, in particular in the simulation of QCD at finitebaryon density, applications to ultracold atoms are still in their infancy. Here we examine the applicability of the CL approach for a one- and two-component, three-dimensional non-relativistic Bose gas in thermal equilibrium, below and above the Bose-Einstein phase transition. By comparison with analytic descriptions at the Gaussian level, including Bogoliubov and Hartree-Fock theory, we find that the method allows computing reliably and efficiently observables in the regime of experimentally accessible parameters. Close to the transition, quantum corrections lead to a shift of the critical temperature which we reproduce within the numerical range known in the literature. With this work, we aim to provide a first test of CL as a potential out-of-the-box tool for the simulation of experimentally realistic situations, including trapping geometries and multicomponent/-species models.

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arXiv2023

Universal dynamics and non-thermal fixed points in quantum fluids far from equilibrium

Closed quantum systems far from thermal equilibrium can show universal dynamics near attractor solutions, known as non-thermal fixed points, generically in the form of scaling behavior in space and time. A systematic classification and comprehensive understanding of such scaling solutions are tasks of future developments in non-equilibrium quantum many-body theory. In this tutorial review, we outline several analytical approaches to non-thermal fixed points and summarize corresponding numerical and experimental results. The analytic methods include a non-perturbative kinetic theory derived within the two-particle irreducible effective-action formalism, as well as a low-energy effective field theory framework. As one of the driving forces of this research field are numerical simulations, we summarize the main results of exemplary cases of universal dynamics in ultracold Bose gases. This encompasses quantum vortex ensembles in turbulent superfluids as well as recently observed real-time instanton solutions in one-dimensional spinor condensates.

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arXiv2023

Simulating the Berezinskii-Kosterlitz-Thouless Transition with Complex Langevin

Numerical simulations of the full quantum properties of interacting many-body systems by means of field-theoretic Monte-Carlo techniques are often limited due to a sign problem. Here we simulate properties of a dilute two-dimensional Bose gas in the vicinity of the Berezinskii-Kosterlitz-Thouless (BKT) transition by means of the Complex Langevin (CL) algorithm, thereby extending our previous CL study of the three-dimensional Bose gas to the lower-dimensional case. The purpose of the paper is twofold. On the one hand, it adds to benchmarking of the CL method and thus contributes to further exploring the range of applicability of the method. With the respective results, the universality of the equation of state is recovered, as well as the long-wave-length power-law dependence of the single-particle momentum spectrum below the BKT transition. Analysis of the rotational part of the current density corroborates vortex unbinding in crossing the transition. Beyond these measures of consistency we compute quantum corrections to the critical density and chemical potential in the weakly coupled regime. Our results show a shift of these quantities to lower values as compared to those obtained from classical field theory. It points in the opposite direction as compared to the shift of the critical density found by means of the path-integral Monte-Carlo method at larger values of the coupling. Our simulations widen the perspective for precision comparisons with experiment.

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arXiv2022

Non-thermal fixed points of universal sine-Gordon coarsening dynamics

We examine coarsening of field-excitation patterns of the sine-Gordon (SG) model, in two and three spatial dimensions, identifying it as universal dynamics near non-thermal fixed points. The SG model is relevant in many different contexts, from solitons in quantum fluids to structure formation in the universe. The coarsening process entails anomalously slow self-similar transport of the spectral distribution of excitations towards low energies, induced by the collisional interactions between the field modes. The focus is set on the non-relativistic limit exhibiting particle excitations only, governed by a Schrödinger-type equation with Bessel-function non-linearity. The results of our classical statistical simulations suggest that, in contrast to wave turbulent cascades, in which the transport is local in momentum space, the coarsening is dominated by rather non-local processes corresponding to a spatial containment in position space. The scaling analysis of a kinetic equation obtained with path-integral techniques corroborates this numerical observation and suggests that the non-locality is directly related to the slowness of the scaling in space and time. Our methods, which we expect to be applicable to more general types of models, could open a long-sought path to analytically describing universality classes behind domain coarsening and phase-ordering kinetics from first principles, which are usually modelled in a near-equilibrium setting by a phenomenological diffusion-type equation in combination with conservation laws.

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