Related papers: Quantum-Classical Liouville Dynamics in the Mappin…
In the case of a quantum-classical hybrid system with a finite number of degrees of freedom, the problem of characterizing the most general dynamical semigroup is solved, under the restriction of being quasi-free. This is a generalization…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
We recently derived a spin-mapping approach for treating the nonadiabatic dynamics of a two-level system in a classical environment [J. Chem. Phys. 151, 044119 (2019)] based on the well-known quantum equivalence between a two-level system…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
A novel method is introduced in order to treat the dissipative dynamics of quantum systems interacting with a bath of classical degrees of freedom. The method is based upon an extension of the Nos\`e-Hoover chain (constant temperature)…
In quantum many-body theory no generic microscopic principle at the origin of complex dynamics is known. Quite opposed, in classical mechanics the theory of non-linear dynamics provides a detailed framework for the distinction between…
We consider the class of non-Hamiltonian and dissipative statistical systems with distributions that are determined by the Hamiltonian. The distributions are derived analytically as stationary solutions of the Liouville equation for…
Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement…
The mixed quantum-classical Liouville equation (QCLE) provides an approximate perturbative framework for describing the dynamics of systems with coupled quantum and classical degrees of freedom of disparate thermal wavelengths. The…
Quantum computing offers promising new avenues for tackling the long-standing challenge of simulating the quantum dynamics of complex chemical systems, particularly open quantum systems coupled to external baths. However, simulating such…
The Lindblad equation generalizes the Schr\"{o}dinger equation to quantum systems that undergo dissipative dynamics. The quantum simulation of Lindbladian dynamics is therefore non-unitary, preventing a naive application of state-of-the-art…
The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common…
We show that the dynamics of a closed quantum system obeys the Hamilton variation principle. Even though quantum particles lack well-defined trajectories, their evolution in the Husimi representation can be treated as a flow of…
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…
A general program to show quantum-classical correspondence for bound conservative integrable and chaotic systems is described. The method is applied to integrable systems and the nature of the approach to the classical limit, the…
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using…
A novel mixed quantum-classical approach to simulating nonadiabatic dynamics of molecules at metal surfaces is presented. The method combines the numerically exact hierarchical equations of motion approach for the quantum electronic degrees…
We present a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems consisting of fast and slow degrees of freedom (DOFs) by extending Gutzwiller's trace formula to a…
The Liouville equation is of fundamental importance in the derivation of continuum models for physical systems which are approximated by interacting particles. However, when particles undergo instantaneous interactions such as collisions,…
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…