Related papers: Dynamics of complex quantum systems with energy di…
In this paper, we study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We uncover that the difference of probability depends on the energy in a striking way and show the…
Quantum mechanics of a general one dimensional dissipative system investigated by it's coupling to a Klein-Gordon field as the environment using a minimal coupling method. Heisenberg equation for such a dissipative system containing a…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
We present a theoretical framework called Lorentz quantum mechanics, where the dynamics of a system is a complex Lorentz transformation in complex Minkowski space. In contrast, in usual quantum mechanics, the dynamics is the unitary…
The eigenvalue of the hermitic Hamiltonian is real undoubtedly. Actually, The reality can also be guaranteed by the $PT$-symmetry. The hermiticity and the $PT$-symmetric quantum theory both have requirements regarding the boundary…
For the non-conservative Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg-Weyl algebra can be found. The inclusion of the standard time evolution…
We consider the Heisenberg spin triangle with general coupling coefficients and general spin quantum number $s$. The corresponding classical system is completely integrable. In the quantum case the eigenvalue problem can be reduced to that…
We investigate how quantum coherence can be distributed among the several off-diagonal elements of an arbitrary density matrix. An easily computable quantity that captures this variability notion is proposed and it is argued that it…
We study four distinct families of Gibbs canonical distributions defined on the standard complex, quaternionic, real and classical (nonquantum) two-level systems. The structure function or density of states for any two-level system is a…
Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the…
The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system…
Quantum resonances described by non-Hermitian tridiagonal-matrix Hamiltonians $H$ with complex energy eigenvalues are considered. The method of evaluation of quantities $\sigma_n$ known as the singular values of $H$ is proposed. Its basic…
Quantum dynamics of a general dissipative system investigated by its coupling to a Klein-Gordon type field as the environment by introducing a minimal coupling method. As an example, the quantum dynamics of a damped three dimensional…
We prove two statements about the long time dynamics of integrable Hamiltonian systems. In classical mechanics, we prove the microcanonical version of the Generalized Gibbs Ensemble (GGE) by mapping it to a known theorem and then extend it…
The dissipative quantum electromagnetics is introduced in a comprehensive manner as a field-matter-bath coupling problem. First, the matter is described by a cluster of Lorentz oscillators. Then the Maxwellian free field is coupled to the…
The dynamics of a kicked quantum system undergoing repeated measurements of momentum is investigated. A diffusive behavior is obtained even when the dynamics of the classical counterpart is not chaotic. The diffusion coefficient is…
We consider a random Hamiltonian $H:\Sigma\to\mathbb R$ defined on a compact space $\Sigma$ that admits a transitive action by a compact group $\mathcal G$. When the law of $H$ is $\mathcal G$-invariant, we show its expected free energy…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
Random matrix theory yields valuable insights into the universal features of quantum many-body chaotic systems. Although all-to-all interactions are traditionally studied, many interesting dynamical questions, such as transport of a…
In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how…