相关论文: Commutability between Semiclassical Limit and Adia…
Let the adiabatic invariant of action variable in slow-fast Hamiltonian system with two degrees of freedom have two limiting values along the trajectories as time tends to infinity. The difference of two limits is exponentially small in…
We study the crossover between the mean-field and critical behavior of the two-dimensional Bose gas throughout the fluctuation region of the Berezinskii--Kosterlitz--Thouless phase transition point. We argue that this crossover is described…
We study the adiabatic approximation of the dynamics of a bipartite quantum system with respect to one of the components, when the coupling between its two components is perturbative. We show that the density matrix of the considered…
The criteria for validity of adiabaticity for nonlinear wave equations are considered within the context of atomic matter-waves tunneling from macroscopically populated optical standing-wave traps loaded from a Bose-Einstein condensate. We…
The viability of adiabatic quantum computation depends on the slow evolution of the Hamiltonian. The adiabatic switching theorem provides an asymptotic series for error estimates in $1/T$, based on the lowest non-zero derivative of the…
We rigorously derive multi-pulse interaction laws for the semi-strong interactions in a family of singularly-perturbed and weakly-damped reaction-diffusion systems in one space dimension. Most significantly, we show the existence of a…
We consider the adiabatic limit in quantum mechanics with several avoided crossings. We compute the interferences effects uniformly w.r. to the gaps and the adiabatic parameter. This way we get the asymoptotic expansion of the global…
We consider a two-component immiscible Bose-Einstein condensate with dominating intra-species repulsive density-density interactions. In the ground-state phase of such a system only one condensates is present. This can be viewed as a…
We study the stationary nonlinear Schr\"odinger equation, or Gross-Pitaevskii equation, for a one--dimensional finite square well potential. By neglecting the mean--field interaction outside the potential well it is possible to discuss the…
We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalised super-adiabatic theorem for the automorphism group…
Consider a multichannel closed ring with disorder. In the semiclassical treatment its conductance is given by the Drude formula. Quantum mechanics challenge this result both in the limit of strong disorder (eigenstates are not…
In two-dimensional space there are possibilities for quantum statistics continuously interpolating between the bosonic and the fermionic one. Quasi-particles obeying such statistics can be described as ordinary bosons and fermions with…
We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting operator. We apply this property to four-state…
We develop a theory of non-relativistic bosons in two spatial dimensions with a weak short range attractive interaction. In the limit as the range of the interaction becomes small, there is an ultra-violet divergence in the problem. We…
Near a quantum critical point (QCP) in a metal, strong Fermion-Fermion interactions mediated by soft collective bosons give rise to two competing phenomena: non-Fermi liquid behavior and superconductivity that deviates from conventional BCS…
In a quantum system with a smoothly and slowly varying Hamiltonian, which approaches a constant operator at times $t\to \pm \infty$, the transition probabilities between adiabatic states are exponentially small. They are characterized by an…
The mean-field limit for the dynamics of bosons with random interactions is rigorously studied. It is shown that, for interactions that are almost-surely bounded, the many-body quantum evolution can be replaced in the mean-field limit by a…
We consider the N-body Schr\"{o}dinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work \cite{AmNi}, the mean field limit is translated into a semiclassical problem with a…
The motion of a muon in two centers coulomb field is one of the interesting problems of quantum mechanics. The adiabatic expansion method is powerful approach to study the muonic three-body system. In this investigation the three-body…
We prove an adiabatic theorem for the ground state of the Dicke model in a slowly rotating magnetic field and show that for weak electron-photon coupling, the adiabatic time scale is close to the time scale of the corresponding two level…