Related papers: Quantization of nonlinear non-Hamiltonian systems
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
We study the dynamics of a two-level quantum system interacting with an external electromagnetic field periodic and quasiperiodic in time. The quantum evolution is described exactly by the classical equations of motion of a gyromagnet in a…
Estimating the steady-state properties of open many-body quantum systems is a fundamental challenge in quantum science and technologies. In this work, we present a scalable approach based on semi-definite programming to derive certified…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…
Development of robust quantum control has been challenging and there are numerous obstacles to applying classical robust control to quantum system including bilinearity, marginal stability, state preparation errors, nonlinear figures of…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…
Established methods for characterizing quantum information processes do not capture non-Markovian (history-dependent) behaviors that occur in real systems. These methods model a quantum process as a fixed map on the state space of a…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
We present a dequantization algorithm for the Vlasov--Poisson (VP) system, termed the dequantized particle algorithm, by systematically dequantizing the underlying many-body quantum theory. Starting from the second-quantized Hamiltonian…
The issue of separating Schr\"odinger-type quantum time evolution into a product of holonomic and dynamical parts in the non-adiabatic non-Abelian case is examined. We identify all special cases in which this kind of separation is possible,…
A method, called beatification, is presented for rapidly extracting weakly nonlinear Hamiltonian systems that describe the dynamics near equilibria for systems possessing Hamiltonian form in terms of noncanonical Poisson brackets. The…
We outline an approach that streamlines considerably the construction and analysis of well-behaved nonlinear quantum dynamics, with completely positive extensions to entangled systems. A few notes are added on the issue of quantum…
Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting…
The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium…
Correlations between different partitions of quantum systems play a central role in a variety of many-body quantum systems, and they have been studied exhaustively in experimental and theoretical research. Here, we investigate dynamical…
We explore the quantization of classical models with position-dependent mass (PDM) terms constrained to a bounded interval in the canonical position. This is achieved through the Weyl-Heisenberg covariant integral quantization by properly…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…