Related papers: Higher order moments dynamics for some multimode q…
A binary expression in terms of operators is given which satisfies all the quantum counterparts of the algebraic properties of the classical antibracket. This quantum antibracket has therefore the same relation to the classical antibracket…
A quantum master equation is obtained for identical fermions by including a relaxation term in addition to the mean-field Hamiltonian. [Huang C F and Huang K N 2004 Chinese J. Phys. ${\bf 42}$ 221; Gebauer R and Car R 2004 Phys. Rev. B…
Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups it is possible to study coherent time evolution of isolated quantum…
A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have…
In this work we are motivated by factorization of bosonic quantum dynamics and we study the corresponding Lie algebras, which can potentially be infinite dimensional. To characterize such factorization, we identify conditions for these Lie…
We explicitly calculate the moments t_n of general Heisenberg Hamiltonians up to sixth order. They have the form of finite sums of products of two factors, the first factor being represented by a multigraph and the second factor being a…
We present a general approach to derive Lindblad master equations for a subsystem whose dynamics is coupled to dissipative bosonic modes. The derivation relies on a Schrieffer-Wolff transformation which allows to eliminate the bosonic…
A useful finite-dimensional matrix representation of the derivative of periodic functions is obtained by using some elementary facts of trigonometric interpolation. This NxN matrix becomes a projection of the angular derivative into…
This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\^o integrals with respect to the compensated Poisson process.…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the…
This paper extends the model reduction method by the operator projection to the three-dimensional special relativistic Boltzmann equation. The derivation of arbitrary order moment system is built on our careful study of infinite families of…
We construct a broad class of completely positive maps and Go\-rini--Kossakowski--Sudarshan-Lindblad generators for fermionic systems induced by linear transformations of system and environment modes. For these maps, we derive explicit…
Exact solutions of time-dependent Schr\"odinger equation in presence of time-dependent potential is defined by point transformation and separation of variables. Energy and Heisenberg uncertainty relation are pursued for time-independent…
It is shown that the initial conditions in the quasi-Heisenberg quantization scheme can be set at the initial cosmological singularity per se. This possibility is provided by finiteness of some quantities, namely momentums of the dynamical…
We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent bundles, ${\rm…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
We construct a generalised expression for the normal ordering of (a+a^{\dagger})^{m} for integral values of m and use the result to study the quantum anharmonic oscillator problem in the Heisenberg approach. In particular, we derive…
We present a consistent formalism to describe the dynamics of hybrid systems with mixed classical and quantum degrees of freedom. The probability function of the system, which, in general, will be a combination of the classical distribution…
We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle…