相关论文: Bogoliubov transformation for distinguishable part…
The transfer operator due to Bogomolny provides a convenient method for obtaining a semiclassical approximation to the energy eigenvalues of a quantum system, no matter what the nature of the analogous classical system. In this paper, the…
The elements of the class of non-homogeneous differential operators which are based on the same vector field, when viewed as acting on appropriate Hilbert spaces, are shown to be isomorphic to each other. It shown that the replacement of a…
The quantum instability of the mean-field theory for identical bosons is shown to be described by an appropriate Bogoliubov transformation. A connection between the quantum and classical linear stability theories is indicated. It is argued…
Following the ideas N. N. Bogoliubov used to derive the classical and quantum nonlinear kinetic equations, we give an alternative derivation of the Redfield quantum linear master equation, which is widely used in the theory of open quantum…
An approach for $q$-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an *-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov…
We review the Bogoliubov theory in the context of recent experiments, where atoms are scattered from a Bose-Einstein Condensate into two well-separated regions. We find the full dynamics of the pair-production process, calculate the first…
It is usually accepted that quantum dynamics described by Schrodinger equation that determines the evolution of states from one Cauchy surface to another is unitary. However, it has been known for some time that this expectation is not…
A one-parameter symplectic group $\{e^{t\dA}\}_{t\in\RR}$ derives proper canonical transformations on a Boson Fock space. It has been known that the unitary operator $U_t$ implementing such a proper canonical transformation gives a…
The classic Bogoliubov theory of weakly interacting Bose gases rests upon the assumption that nearly all the bosons condense into the lowest quantum state at sufficiently low temperatures. Here we develop a generalized version of Bogoliubov…
We consider a massless scalar field in 1+1 dimensions satisfying a Robin boundary condition (BC) at a non-relativistic moving boundary. We derive a Bogoliubov transformation between input and output bosonic field operators, which allows us…
We study the time evolution of the Nelson model in a mean-field limit in which N non-relativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the…
Systems of interest in physics are usually composed by a very large number of interacting particles. At equilibrium, these systems are described by stationary states of the many-body Hamiltonian (at zero temperature, by the ground state).…
Starting from first principle many-body quantum dynamics, we show that the dynamics of Bose-Einstein condensates can be approximated by the time-dependent nonlinear Gross-Pitaevskii equation, giving a bound on the rate of the convergence.…
In the Bogoliubov theory a condensate initially prepared in its ground state described by stationary Bogoliubov vacuum and later perturbed by a time-dependent potential or interaction strength evolves into a time-dependent excited state…
In this paper we consider the occupation number of induced quasi-particles produced during a time-dependent process using three-different methods: Instantaneous diagonalization, Bogolyubov transformation between two different vacua, and the…
A linear quantum dynamical theory for squeezing the output of the trapped Bose-Einstein condensate is presented with the Bogoliubov approximation. We observe that the non-classical properties, such as sub-Poisson distribution and quadrature…
In the present paper, we study quantum Sobolev spaces whose elements are operators of the Hilbert-Schmidt class. We construct these Sobolev spaces from the Fourier transform for operators. Next, we obtain continuous embedding theorems.…
A master equation containing a nonlinear term that gives rise to disentanglement has been recently investigated. In this study, a modified version, which is applicable for indistinguishable particles, is proposed, and explored for both the…
Darboux transformation of a second-order linear differential operator is a well-known technique with many applications in mathematics and physics. We study Darboux transformation from the point of view of Markov semigroups of diffusion…
We present a new method for finding isolated exact solutions of a class of non-adiabatic Hamiltonians of relevance to quantum optics and allied areas. Central to our approach is the use of Bogoliubov transformations of the bosonic fields in…