Related papers: Dynamics of mixed classical-quantum systems, geome…
Preserving quantum coherence with the increase of a system's size and complexity is a major challenge. Molecules, with their diverse sizes and complexities and many degrees of freedom, are an excellent platform for studying the transition…
A filtering problem for a class of quantum systems disturbed by a classical stochastic process is investigated in this paper. The classical disturbance process, which is assumed to be described by a linear stochastic differential equation,…
The dynamics of states representing arbitrary N-level quantum systems, including dissipative systems, can be modelled exactly by the dynamics of classical coupled oscillators. There is a direct one-to-one correspondence between the quantum…
Based on Koopman formalism for classical statistical mechanics, we propose a formalism to define hybrid quantum-classical dynamical systems by defining (outer) automorphisms of the C*-algebra of hybrid operators and realizing them as linear…
We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…
The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…
The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it…
The popular method of Nose and Hoover to create canonically distributed positions and momenta in classical molecular dynamics simulations is generalized to a genuine quantum system of infinite dimensionality. We show that for the quantum…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…
This article provides an accessible illustration of the measurement approach to the study of the quantum-classical transition suitable for beginning graduate students. As an example, we apply it to a quantum system with a general quadratic…
Starting from the geometric description of quantum systems, we propose a novel approach to time-independet dissipative quantum processes according to which the energy is dissipated but the coherence of the states is preserved. Our proposal…
A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
The two main notions of control in quantum programming languages are often referred to as "quantum" control and "classical" control. With the latter, the control flow is based on classical information, potentially resulting from a quantum…
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g.,…
We present a pedagogical work-in-progress. This textbook aims to introduce Hilbert space representations for quantum and classical dynamics, outlining the mathematical foundations, practical guidance, and Python implementation of dynamical…
The dynamic of a classical system can be expressed by means of Poisson brackets. In this paper we generalize the relation between the usual non covariant Hamiltonian and the Poisson brackets to a covariant Hamiltonian and new brackets in…