Related papers: Quantum Dynamics of Complex Hamiltonians
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the…
The Hamiltonian of an isolated quantum mechanical system determines its dynamics and physical behaviour. This study investigates the possibility of learning and utilising a system's Hamiltonian and its variational thermal state estimation…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a…
Existing approaches to analogue quantum simulations of time-dependent quantum systems rely on perturbative corrections to quantum simulations of time-independent quantum systems. We overcome this restriction to perturbative treatments with…
The study of phase transitions in dissipative quantum systems based on the Liouvillian is often hindered by the difficulty of constructing a time-local master equation when the system-environment coupling is strong. To address this issue,…
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…
We analyze the new equation of motion for the damped oscillator. It differs from the standard one by a damping term which is nonlocal in time and hence it gives rise to a system with memory. Both classical and quantum analysis is performed.…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…
By taking a Klein-Gordon field as the environment of an harmonic oscillator and using a new method for dealing with quantum dissipative systems (minimal coupling method), the quantum dynamics and radiation reaction for a quantum damped…
A variety of dynamics in nature and society can be approximately treated as a driven and damped parametric oscillator. An intensive investigation of this time-dependent model from an algebraic point of view provides a consistent method to…
We study the dissipative dynamics of a single quantum harmonic oscillator subjected to a parametric driving with in an effective Hamiltonian approach. Using Liouville von Neumann approach, we show that the time evolution of a parametrically…
We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several bi-infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
We study a quantum theory with complex time parameter and non-Hermitian Hamiltonian structure. In this theory, the real part of the complex time is equal to `usual' physical time, whereas the imaginary one is proportional to inverse…
A condition to have a real spectrum for a non-Hermitian Hamiltonian is given. As special cases, it is shown that the condition is reduced to Hermiticity and PT symmetric conditions.
We determine the late-time dynamics of a generic spin ensemble with inhomogeneous broadening - equivalently, qubits with arbitrary Zeeman splittings - coupled to a dissipative environment with strength decreasing as $1/t$. The approach to…
A stable physical system has an energy spectrum that is bounded from below. For quantum systems, the dangerous states of unboundedly low energies should decouple and become null. We propose the principle of nullness and apply it to the…
A method to construct non-dissipative non-Dirac-hermitian relativistic quantum system that is isospectral with a Dirac-hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical…