41 research outputs found
Universal vortex statistics and stochastic geometry of Bose-Einstein condensation
peer reviewedThe cooling of a Bose gas in finite time results in the formation of a Bose-Einstein condensate that is spontaneously proliferated with vortices. We propose that the vortex spatial statistics is described by a homogeneous Poisson point process (PPP) with a density dictated by the Kibble-Zurek mechanism (KZM). We validate this model using numerical simulations of the two-dimensional stochastic Gross-Pitaevskii equation (SGPE) for both a homogeneous and a hard-wall trapped condensate. The KZM scaling of the average vortex number with the cooling rate is established along with the universal character of the vortex number distribution. The spatial statistics between vortices is characterized by analyzing the two-point defect-defect correlation function, the corresponding spacing distributions, and the random tessellation of the vortex pattern using the Voronoi cell area statistics. Combining the PPP description with the KZM, we derive universal theoretical predictions for each of these quantities and find them in agreement with the SGPE simulations. Our results establish the universal character of the spatial statistics of point-like topological defects generated during a continuous phase transition and the associated stochastic geometry
One-Dimensional Quantum Systems with Ground State of Jastrow Form Are Integrable
Exchange operator formalism describes many-body integrable systems using phase-space variables involving an exchange operator that acts on any pair of particles. We establish an equivalence between models described by exchange operator formalism and the complete infinite family of parent Hamiltonians describing quantum many-body models with ground states of Jastrow form. This makes it possible to identify the invariants of motion for any model in the family and establish its integrability, even in the presence of an external potential. Using this construction we establish the integrability of the long-range Lieb-Liniger model, describing bosons in a harmonic trap and subject to contact and Coulomb interactions in one dimension.We further identify a variety of models exemplifying the integrability of Hamiltonians in this family
Universal symmetry breaking passes the superfluid test
peer reviewedThe Kibble–Zurek mechanism is a key framework for describing the dynamics of continuous phase transitions. Recent experiments with ultracold gases, employing alternative methods to create a superfluid, highlight its universality
Probing quantum chaos in multipartite systems
Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting statistics of the local, total, and interaction energies. As in the spectral form factor, signatures of quantum chaos in the time domain dictate a dip-ramp-plateau structure in the characteristic function, i.e., the Fourier transform of the eigenvalue distribution. With this approach, we explore the fate of chaos in interacting subsystems that are locally maximally chaotic. Global quantum chaos can be suppressed at strong coupling, as illustrated with coupled copies of random-matrix Hamiltonians and of the Sachdev-Ye-Kitaev model. Our method is amenable to experimental implementation using single-qubit interferometry
Probing quantum chaos in multipartite systems
Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting statistics of the local, total, and interaction energies. As in the spectral form factor, signatures of quantum chaos in the time domain dictate a dip-ramp-plateau structure in the characteristic function, i.e., the Fourier transform of the eigenvalue distribution. With this approach, we explore the fate of chaos in interacting subsystems that are locally maximally chaotic. Global quantum chaos can be suppressed at strong coupling, as illustrated with coupled copies of random-matrix Hamiltonians and of the Sachdev-Ye-Kitaev model. Our method is amenable to experimental implementation using single-qubit interferometry
Decoherence rate in random Lindblad dynamics
editorial reviewedOpen quantum systems undergo decoherence, which is responsible for the transition from quantum to classical behavior. The time scale in which decoherence takes place can be analyzed using upper limits to its rate. We examine the dynamics of open chaotic quantum systems governed by random Lindblad operators sourced from Gaussian and Ginibre ensembles with Wigner-Dyson symmetry classes. In these systems, the ensemble-averaged purity decays monotonically as a function of time. This decay is governed by the decoherence rate, which is upper-bounded by the dimension of their Hilbert space and is independent of the ensemble symmetry. These findings hold upon mixing different ensembles, indicating the universal character of the decoherence rate limit. Moreover, our findings reveal that open chaotic quantum systems governed by random Lindbladians tend to exhibit the most rapid decoherence, regardless of the initial state. This phenomenon is associated with the concentration of the decoherence rate near its upper bound. Our work identifies primary features of decoherence in dissipative quantum chaos, with applications ranging from quantum foundations to high-energy physics and quantum technologies
Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition
In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scales with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZM have recently been unveiled: The number distribution of topological defects has been shown to follow a binomial distribution, in which all cumulants inherit the universal power-law scaling with the quench rate, with cumulant rations being constant. In this work, we analyze the role of boundary conditions in the statistics of topological defects. In particular, we consider a lattice system with nearest-neighbor interactions subject to soft antiperiodic, open, and periodic boundary conditions implemented by an energy penalty term. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate that is independent of the boundary conditions except for an additive term, which becomes prominent in the limit of slow quenches, leading to the breaking of power-law behavior. We test our theoretical predictions with a one-dimensional scalar theory on a lattice
Universal Breakdown of Kibble-Zurek Scaling in Fast Quenches across a Phase Transition
The crossing of a continuous phase transition in finite time gives rise to
the formation of topological defects described by the Kibble-Zurek mechanism
(KZM) in the limit of slow quenches. The KZM predicts a universal power-law
scaling of their density with the quench time in which the transition is
crossed. We focus on the deviations from KZM experimentally observed in rapid
quenches and establish their universality. While KZM scaling holds below a
critical quench rate, for faster quenches the defect density and the freeze-out
time become independent of the quench rate and exhibit a universal power-law
scaling with the final value of the control parameter. These predictions are
verified in paradigmatic scenarios using a -theory and a model of a
strongly-coupled superconducting ring.Comment: 7+1 pp, 5 figure
Kibble-Zurek mechanism for nonequilibrium phase transitions in driven systems with quenched disorder
We numerically study the density of topological defects for a two-dimensional
assembly of particles driven over quenched disorder as a function of quench
rate through the nonequilibrium phase transition from a plastic disordered
flowing state to a moving anisotropic crystal. A dynamical ordering transition
of this type occurs for vortices in type-II superconductors, colloids, and
other particle-like systems in the presence of random disorder. We find that on
the ordered side of the transition, the density of topological defects
scales as a power law, , where is the
time duration of the quench across the transition. This type of scaling is
predicted in the Kibble-Zurek mechanism for varied quench rates across a
continuous phase transition. We show that scaling with the same exponent holds
for varied strengths of quenched disorder. The value of the exponent can be
connected to the directed percolation universality class. Our results suggest
that the Kibble-Zurek mechanism can be applied to general nonequilibrium phase
transitions.Comment: 7 pages, 7 figure