Related papers: Mapping quantum-classical Liouville equation: proj…
A model, based on a noncommutative geometry, unifying general relativity with quantum mechanics, is further develped. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators. It is…
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
The von Neumann evolution equation for density matrix and the Moyal equation for the Wigner function are mapped onto evolution equation for optical tomogram of quantum state. The connection with known evolution equation for symplectic…
We propose a protocol for coherently transferring non-Gaussian quantum states from optical field to a mechanical oscillator. The open quantum dynamics and continuous-measurement process, which can not be treated by the…
We consider the quantum and classical Liouville dynamics of a non-integrable model of two coupled spins. Initially localised quantum states spread exponentially to the system dimension when the classical dynamics are chaotic. The long-time…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
Starting with the first-order singular Lagrangian, the problem of the quantization of a dynamical system constrained to a submanifold embedded in the higher-dimensional Euclidean space is investigated within the framework of operatorial…
We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving…
Continuous time quantum walks on exponentially large, sparse graphs form a powerful paradigm for quantum computing: On the one hand, they can be efficiently simulated on a quantum computer. On the other hand, they are themselves…
The quantum Liouville equation, which describes the phase space dynamics of a quantum system of fermions, is analyzed from statistical point of view as a particular example of the Kramers-Moyal expansion. Quantum mechanics is extended to…
By means of studying the evolution equation for the Wigner distributions of quantum dissipative systems we derive the quantum corrections to the classical Liouville dynamics, taking into account the standard quantum friction model. The…
Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of…
Numerical simulation of individual open quantum systems has proven advantages over density operator computations. Quantum state diffusion with a moving basis (MQSD) provides a practical numerical simulation method which takes full advantage…
We consider Markovian open quantum dynamics with weak unitary symmetries. Starting from the quantum master equation for the system alone, it is known that the joint dynamics of the system and its environment can be obtained by dilation,…
Starting with the first-order singular Lagrangian, the canonical structures of the noncommutative quantum system on a submanifold embedded in the higher-dimensional Euclidean space are investigated with the projection operator method (POM)…
We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of…
Nonadiabatic dynamical processes are one of the most important quantum mechanical phenomena in chemical, materials, biological, and environmental molecular systems, where the coupling between different electronic states is either inherent…
The information of quantum pathways can be extracted in the framework of the Hamiltonian-encoding and Observable-decoding method. For closed quantum systems, only off-diagonal elements of the Hamiltonian in the Hilbert space is required to…