相关论文: On the semiclassical evolution of quantum operator…
We analyse the dynamics of expectation values of quantum observables for the time-dependent semiclassical Schr\"odinger equation. To benefit from the positivity of Husimi functions, we switch between observables obtained from Weyl and…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
The Herman--Kluk propagator is a popular semi-classical approximation of the unitary evolution operator in quantum molecular dynamics. In this paper we formulate the Herman--Kluk propagator as a phase space integral and discretise it by…
We systematically derive a linear quantum collision operator for the spinorial Wigner transport equation from the dynamics of a composite quantum system. For suitable two particle interaction potentials, the particular matrix form of the…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
We construct the quantum mechanical evolution operator in the Functional Schrodinger picture - the kernel - for a scalar field in spatially homogeneous FLRW spacetimes when the field is a) free and b) coupled to a spacetime dependent source…
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…
We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system evolves via either Hamiltonian propagators or…
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done by a projective representation of double-phase space, and we…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
A uniform semiclassical propagator is used to time evolve a wavepacket in a smooth Hamiltonian system at energies for which the underlying classical motion is chaotic. The propagated wavepacket is Fourier transformed to yield a scarred…
In this article, we study two different types of operators, the localization operator and Weyl transform, on the reduced Heisenberg group with multidimensional center $\mathcal{G}$. The group $\mathcal{G}$ is a quotient group of…
We consider diffusive systems, regarded as input/output systems with a kernel given as the Fourier--Borel transform of a measure in the left half-plane. Associated with these are a family of weighted Hankel integral operators, and we…
Wigner phase space quasi-probability distribution function is a Fourier transform related to a given quantum mechanical wave function. It is shown that for the wave functions of type $\psi (q)=e^{-aq^2}\phi (q)$, the Wigner function can be…
We derive a semi-classical nonequilibrium work identity by applying the Wigner-Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us, to the leading order in $\hbar$, to overcome the problem of…
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
The new numerical approach for consideration of quantum dynamics and calculations of the average values of quantum operators and time correlation functions in the Wigner representation of quantum statistical mechanics has been developed.…
Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schr\"odinger…
A system of $N$ non-canonical dynamically free 3D harmonic oscillators is studied. The position and the momentum operators (PM-operators) of the system do not satisfy the canonical commutation relations (CCRs). Instead they obey the weaker…
We introduce a hybrid quantum-classical framework for efficiently implementing approximate unitary dilations of non-unitary operators with enhanced noise resilience. The method embeds a target non-unitary operator into a subblock of a…