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We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian)…
We consider a quantum system consisting of a one-dimensional chain of M identical harmonic oscillators with natural frequency $\omega$, coupled by means of springs. Such systems have been studied before, and appear in various models. In…
In the framework of the Lindblad theory for open quantum systems, a master equation for the quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived for the case when the…
In this paper we present a comprehensive analysis of the coherence phenomenon of two coupled dissipative oscillators. The action of a classical driving field on one of the oscillators is also analyzed. Master equations are derived for both…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
When studying out-of-equilibrium systems, one often excites the dynamics in some degrees of freedom while removing the excitation in others through damping. In order for the system to converge to a statistical steady state, the dynamics…
Quantum computers and simulators can potentially outperform classical computers in finding ground states of classical and quantum Hamiltonians. However, if this advantage can persist in the presence of noise without error correction remains…
Quantum sensing utilizes quantum systems as sensors to capture weak signal, and provides new opportunities in nowadays science and technology. The strongest adversary in quantum sensing is decoherence due to the coupling between the sensor…
We study the connection between Lagrangian and Hamiltonian descriptions of closed/open dynamics, for a collection of particles with quadratic interaction (closed system) and a sub-collection of particles with linear damping (open system).…
The Ullersma model for the damped harmonic oscillator is coupled to the quantised electromagnetic field. All material parameters and interaction strengths are allowed to depend on position. The ensuing Hamiltonian is expressed in terms of…
The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master…
Starting from the Wigner-Moyal equation coupled to Poisson's equation, a simplified set of equations describing nonlinear Landau damping of Langmuir waves is derived. This system is studied numerically, with a particular focus on the…
The dissipative dynamics of a quantum bistable system coupled to a Ohmic heat bath is investigated beyond the spin-boson approximation. Within the path-integral approach to quantum dissipation, we propose an approximation scheme which…
We present a unified quantum open system framework for lossy plasmonic cavities in which coherent dynamics, relaxation, dephasing, and irreversible absorption are treated on equal footing. The Dyson equation for the cavity photon propagator…
The connections between standard theoretical tools used to study open quantum systems can sometimes seem opaque. Whether it is a Lindblad master equation, the equation of motion for the Wigner function or a dissipative Keldysh action,…
We develop a quantum model based on the correspondence between energy distribution between harmonic oscillators and the partition of an integer number. A proper choice of the interaction Hamiltonian acting within this manifold of states…
For a free falling particle moving in a media which has quadratic velocity force effect on the particle, two equivalent constants of motion, with units of energy, two Lagrangians, and two Hamiltonians are deduced. These quantities describe…
The metaphor of a clock in physics describes near-equilibrium reversible phenomena such as an oscillating spring. It is surprising that for chemical and biological clocks the focus has been exclusively on the far-from-equilibrium…
In this paper we present a method with which it is possible to describe a dissipative system in Lagrangian formalism, without the trouble of finding the proper way to model the environment. The concept of the presented method is to create a…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…