We consider the Landau-Teller model, which is a prototype for the exchanges of energy, in molecular collisions, between internal degrees of freedom and those of the center of mass. We show that the statistics of the energy exchanges computed through the dynamics over a finite time is of the Lévy type for high enough frequencies of the internal motions, while it reduces to the familiar Gaussian one in the limit of low frequencies. The relevance for the definition of the times of relaxation to equilibrium is also pointed out.

We discuss stability and phase coherence of 1D trapped Bose gases and find that inelastic decay processes, such as three-body recombination, are suppressed in the strongly interacting (Tonks-Girardeau) and intermediate regimes. This is promising for achieving these regimes with a large number of particles. ”Fermionization” of the system reduces the phase coherence length, and at $T=0$ the gas is fully phase coherent only deeply in the weakly interacting (Gross-Pitaevskii) regime.

It is shown, under the assumption of the possibility to perform an arbitrary local operation, that all nonlocal variables related to two or more separate sites can be measured instantaneously, except for a finite time required for bringing to one location the classical records from these sites which yield the result of the measurement. It is a verification measurement: it yields reliably the eigenvalues of the nonlocal variables, but it does not prepare the eigenstates of the system.

We derive an inequality governing “long-range” order for a localized Bose-condensed state, relating the condensate fraction at a given temperature with effective curvature radius of the condensate and total particle number. For the specific example of a one-dimensional, harmonically trapped dilute Bose condensate, it is shown that the inequality gives an explicit upper bound for the Thomas-Fermi condensate size which may be tested in current experiments.

We have investigated the constructive roles of temporal noise, spatial disorder, and spatiotemporal fluctuation on the formation of spiral waves. Noise-sustained spiral waves are observed, the order of which passes a maximum with the increment of noise intensity, showing spatiotemporal coherent resonance. Moreover, we find that spatiotemporal fluctuation is much more favorable for the ordering process than temporal-noise only or spatial-disorder only. We demonstrate that this phenomenon shows the disadvantageous effect of spatial or temporal memory of noise.

Interactions never lower the ground state kinetic energy of a quantum system below the noninteracting value. However, at nonzero temperature, where the system occupies a thermal distribution of states, interactions can reduce the kinetic energy. This can be demonstrated from a first order weak coupling expansion. Simulations (both variational and restricted path integral Monte Carlo) of the electron gas model and dense hydrogen confirm this and show that in contrast to the ground state case, at nonzero temperature the population of low momentum states can be increased relative to the free Fermi distribution. This effect is not seen in simulations of liquid ${}^{\mathrm{3}}\mathrm{H}\mathrm{e}$.

We report the formation of Bose-Einstein condensates into nonequilibrium states. Our condensates are much longer than equilibrium condensates with the same number of atoms, show strong phase fluctuations, and have a dynamical evolution similar to that of quadrupole shape oscillations of regular condensates. The condensates emerge in elongated traps as the result of local thermalization when the nucleation time is short compared to the axial oscillation time. We introduce condensate focusing as a new method to extract the phase-coherence length of Bose-Einstein condensates.

Requiring that a Hamiltonian be Hermitian is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the less restrictive and more physical condition of space-time reflection symmetry ($\mathcal{P}\mathcal{T}$ symmetry). One might expect a non-Hermitian Hamiltonian to lead to a violation of unitarity. However, if $\mathcal{P}\mathcal{T}$ symmetry is not spontaneously broken, it is possible to construct a previously unnoticed symmetry $\mathcal{C}$ of the Hamiltonian. Using $\mathcal{C}$, an inner product whose associated norm is positive definite can be constructed. The procedure is general and works for any $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian. Observables exhibit $\mathcal{C}\mathcal{P}\mathcal{T}$ symmetry, and the dynamics is governed by unitary time evolution. This work is not in conflict with conventional quantum mechanics but is rather a complex generalization of it.

We study the properties of quantum entanglement in moving frames, and show that, because spin and momentum become mixed when viewed by a moving observer, the entanglement between the spins of a pair of particles is not invariant. We give an example of a pair, fully spin entangled in the rest frame, which has its spin entanglement reduced in all other frames. Similarly, we show that there are pairs whose spin entanglement increases from zero to maximal entanglement when boosted. While spin and momentum entanglement separately are not Lorentz invariant, the joint entanglement of the wave function is.

We study the stability of quantum states of macroscopic systems of finite volume $V$. By using both the locality and huge degrees of freedom, we show the following: (i) If square fluctuation of every additive operator is $O(V)$ or less for a pure state, then it is not fragile for any weak classical noises or weak perturbations from environments. (ii) If square fluctuation of some additive operator is $O(V^2)$ for a pure state, then it is fragile for some of these. (iii) If a state, pure or mixed, has the “cluster property,” then it is stable against local measurements, and vice versa. Among many applications, we discuss the mechanism of symmetry-breaking in finite systems.

We give a simple unified theory of vortex nucleation and vortex lattice formation in which (i) the thermal cloud plays a crucial role; (ii) the basic process is due to growth of the condensate from a rotating thermal cloud, which provides gain for certain surface modes of nonzero angular momentum; (iii) vortices appear initially as the result of a linear interference between the far fields of the condensate and the surface modes; and (iv) the description applies from the initiation process up to the final stabilization of the lattice. We have simulated the growth of vortex lattices from a rotating thermal cloud, and their production using a rotating trap.

We derive tight quadratic inequalities for all kinds of hybrid separable-inseparable $n$-particle density operators on an arbitrary dimensional space. This methodology enables us to derive a tight quadratic inequality as tests for full $n$-partite entanglement in various Bell-type correlation experiments on the systems that may not be identified as a collection of qubits, e.g., those involving photons measured by incomplete detectors. It is also proved that when the two measured observables are assumed to precisely anticommute, a stronger quadratic inequality can be used as a witness of full $n$-partite entanglement.

Exact solvability is claimed for nonlinear replica $\sigma$ models derived in the context of random matrix theories. Contrary to other approaches reported in the literature, the framework outlined does not rely on traditional “replica symmetry breaking” but rests on a previously unnoticed exact relation between replica partition functions and Painlevé transcendents. While expected to be applicable to matrix models of arbitrary symmetries, the method is used to treat fermionic replicas for the Gaussian unitary ensemble (GUE), chiral GUE (symmetry classes A and AIII in Cartan classification) and Ginibre’s ensemble of complex non-Hermitian random matrices. Further applications are briefly discussed.

Following a suggestion by Orzel et al. [Science 291, 2386 (2001)], we analyze bosons in an optical lattice undergoing a sudden parameter change from the Mott to superfluid phase. We introduce a modified coherent states path integral to describe both phases. The saddle point theory yields collective oscillations of the uniform superfluid order parameter. We calculate its damping rate by phason pair emission. In two dimensions the overdamped region largely overlaps with the quantum critical region. Measurements of critical dynamics on the Mott side are proposed.

We consider diffusion-limited reactions $A_i+A_j\to \varnothing$ ($1\le i<j\le q$) in $d$ space dimensions. For $q>2$ and $d\ge 2$, we argue that the asymptotic density decay for such mutual annihilation processes with equal rates and initial densities is the same as for single-species pair annihilation $A+A\to \varnothing$. In $d=1$, however, particle segregation occurs for all $q<\infty$. The total density decays according to a $q$ dependent power law, $\rho (t)\sim t^{-\alpha (q)}$. Within a simplified version of the model $\alpha (q)=(q-1)/2q$ can be determined exactly. Our findings are supported through Monte Carlo simulations.

We study the expansion of a dilute ultracold sample of fermions initially trapped in an anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In particular, the time evolution of the deformation of the expanding cloud behaves quite differently depending on whether the system is in the normal or in the superfluid phase. For the superfluid phase, we predict an inversion of the deformation of the sample, similar to what happens with Bose-Einstein condensates. Vice versa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.

We show that it is possible to construct the Feynman propagator for a free particle in one dimension, without quantization, from a single continuous space-time path.

We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length $a_{\mathrm{o}\mathrm{s}\mathrm{c}}$. The atoms are assumed to interact through a short-range potential with a scattering length $a$, and the short-distance behavior of the three-body wave function is characterized by a parameter $\theta$. For large positive $a/a_{\mathrm{o}\mathrm{s}\mathrm{c}}$, the energies of states that, in the absence of the trap, correspond to three free atoms approach values independent of $a$ and $\theta$. For other states, the $\theta$ dependence of the energy is strong, but the energy is independent of $a$ for $|a/a_{\mathrm{o}\mathrm{s}\mathrm{c}}|\gg 1$.

We establish a necessary and sufficient condition for averages over complex-valued weight functions on $R^N$ to be represented as statistical averages over real, non-negative probability weights on $C^N$. Using this result, we show that many path integrals for time-ordered expectation values of bosonic degrees of freedom in real-valued time can be expressed as statistical averages over ensembles of paths with complex-valued coordinates, and then speculate on possible consequences of this result for the relation between quantum and classical mechanics.

We argue that on its face, entanglement theory satisfies laws equivalent to thermodynamics if the theory can be made reversible by adding certain bound entangled states as a free resource during entanglement manipulation. Subject to plausible conjectures, we prove that this is not the case in general, and discuss the implications of this for the thermodynamics of entanglement.