相关论文: Effective Hamiltonian and unitarity of the S matri…
A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second order symmetries, is considered. After separation of variables, the one-dimensional matrix…
We consider a Hamiltonian $ H = H_0+ V $, in which $ H_0$ is a given non-random Hermitian matrix,and $V$ is an $N \times N$ Hermitian random matrix with a Gaussian probability distribution.We had shown before that Dyson's universality of…
The current applications of non-Hermitian but ${\cal PT}-$symmetric Hamiltonians $H$ cover several, mutually not too closely connected subdomains of quantum physics. Mathematically, the split between the open and closed systems can be…
Quantum bound-state energies are assumed generated by PT-symmetric Hamiltonians H where P is, typically, parity. It is known that their spectrum only remains real and observable (i.e., in the language of physics, the PT-symmetry remains…
We consider the time-dependent Schr\"odinger equation on a Riemannian manifold $\mathcal{A}$ with a potential that localizes a certain class of states close to a fixed submanifold $\mathcal{C}$. When we scale the potential in the directions…
Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states…
We give a formula to calculate a matrix element of a conserved current in the effective quantum mechanics defined by the wave function equivalent potentials proposed by HAL QCD collaboration. As a first step, a non-relativistic field theory…
A family of effective actions in Hamiltonian form is derived for a self-gravitating sphere of isotropic homogeneous dust. Starting from the Einstein-Hilbert action for barotropic perfect fluids and making use of the symmetry and equation of…
Variation of coupling constants of integrable system can be considered as canonical transformation or, infinitesimally, a Hamiltonian flow in the space of such systems. Any function $T(\vec p, \vec q)$ generates a one-parametric family of…
The problem of one pair of identical nucleons sitting in ${\cal N}$ single particle levels of a potential well and interacting through the pairing force is treated introducing even Grassmann variables. The eigenvectors are analytically…
The states of an open quantum system are coupled via the environment of scattering wavefunctions. The complex coupling coefficients $\omega$ between system and environment arise from the principal value integral and the residuum. At high…
For any unitarily invariant convex function F on the states of a composite quantum system which isolates the trace there is a critical constant C such that F(w)<= C for a state w implies that w is not entangled; and for any possible D > C…
A one-to-one correspondence is known to exist between the spectra of the discrete states of the non Hermitian Swanson-type Hamiltonian $ H = {\cal{A}}^{\dagger} {\cal{A}} + \alpha {\cal{A}} ^2 + \beta {\cal{A}}^{\dagger 2} $, ($\alpha \neq…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical-quantum coupling. The proposed model not only…
The entanglement Hamiltonian $H_E$, defined through the reduced density matrix of a subsystem $\rho_A=\exp(-H_E)$, is an important concept in understanding the nature of quantum entanglement in many-body systems and quantum field theories.…
We use a Gaussian wave functional for the ground state to reorder the Hamiltonian into a free part with a variationally determined mass and the rest. Once spontaneous symmetry breaking is taken into account, the residual Hamiltonian can, in…
We show that a polynomial H(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice…
In a complex scattering system with few open channels, say a quantum dot with leads, the correlation properties of the poles of the scattering matrix are most directly related to the internal dynamics of the system. We may ask how to…
A general hamiltonian $H$ of electrons in finite concentration, interacting via any two-body coupling inside a crystal of arbitrary dimension, is considered. For simplicity and without loss of generality, a one-band model is used to account…