Related papers: Density matrices and entropy operator for non-Herm…
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models…
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…
We consider effective operators describing Dark Matter (DM) interactions with Standard Model fermions. In the non-relativistic limit of the DM field, the operators can be organized according to their mass dimension and their velocity…
We derive several entanglement conditions employing non-hermitian operators. We start with two conditions that were derived previously for field mode operators, and use them to derive conditions that can be used to show the existence of…
Quantum Information is a new area of research which has been growing rapidly since last decade. This topic is very close to potential applications to the so called Quantum Computer. In our point of view it makes sense to develop a more…
We study the density of states (DOS) for disordered systems whose spectral statistics can be described by a Gaussian ensemble of almost diagonal Hermitian random matrices. The matrices have independent random entries $ H_{i \geq j} $ with…
In this article we study port-Hamiltonian partial differential equations on certain one-dimensional manifolds. We classify those boundary conditions that give rise to contraction semigroups. As an application we study port-Hamiltonian…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…
We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in…
We extend the formulation of pseudo-Hermitian quantum mechanics to eta-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta. In particular, we give the details of the construction of the physical Hilbert space,…
We consider density matrices which are sums of projectors on states spanning irreducible representations of the permutation group of L sites (eigenstates of permutational invariant quantum system with L sites) and construct the reduced…
A non-Hermitian generalized oscillator model, generally known as the Swanson model, has been studied in the framework of R-deformed Heisenberg algebra. The non-Hermitian Hamiltonian is diagonalized by generalized Bogoliubov transformation.…
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices from indirect measurements, also known as quantum state…
We reconsider the recently proposed connection between density of states in the so-called ``non-hermitian quantum mechanics'' and the localization length for a particle moving in random potential. We argue that it is indeed possible to find…
In this paper, we present extraordinary algebraic and geometrical structures for the Hunter-Saxton equation: infinitely many commuting and non-commuting $x,t$-independent higher order symmetries and conserved densities. Using a recursive…
In this work, we readdress the Dirac equation in the position-dependent mass (PDM) scenario. Here, one investigates the quantum dynamics of non-Hermitian fermionic particles with effective mass assuming a $(1+1)$-dimension flat spacetime.…
As a new approach to efficiently describe correlation effects in the relativistic quantum world we propose to consider reduced density matrix functional theory, where the key quantity is the first-order reduced density matrix (1-RDM). In…
Effective field theories have often been applied to systems with deeply inelastic reactions that produce particles with large momenta outside the domain of validity of the effective theory. The effects of the deeply inelastic reactions have…