Related papers: Some Quantum Dynamical Semi-groups with Quantum St…
We show that provided $n\ne 3$, the involutive Hopf *-algebra $A_u(n)$ coacting universally on an $n$-dimensional Hilbert space has enough finite-dimensional representations in the sense that every non-zero element acts non-trivially in…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
In quantum many-body systems with kinetically constrained dynamics, the Hilbert space can split into exponentially many disconnected subsectors, a phenomenon known as Hilbert-space fragmentation. We study the interplay of such fragmentation…
In conventional Schr\"{o}dinger representation the unitarity of the evolution of bound states is guaranteed by the Hermiticity of the Hamiltonian. A non-unitary isospectral simplification of the Hamiltonian, $\mathfrak{h} \to…
Stationary quantum stochastic process j is introduced as a *-homomorphism embedding an involutive graded algebra $\tilde K=\oplus_{i=1}^{\infty}K_i$ into a ring of (abelian) cohomologies of the one-parameter group $\alpha$ consisting of…
We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical…
A recent characterisation of Fock-adapted contraction operator stochastic cocycles on a Hilbert space, in terms of their associated semigroups, yields a general principle for the construction of such cocycles by approximation of their…
In this paper we study some particular types of matrix Schr\"odinger semigroups of the form $\exp(-it\mathbb{H})$ where $\mathbb{H}\in M_N(\mathbf{C})$ is the Hamiltonian of a given quantum dynamical system modeled in the finite dimensional…
We study a class of finite dimensional quantum dynamical semigroups exp(tL) whose generators L are sums of Lindbladians satisfying the detailed balance condition. Such semigroup arise in the weak coupling (van Hove) limit of Hamiltonian…
We introduce a class of Markovian quantum master equations, able to describe the dissipative dynamics of a quantum system weakly coupled to one or several heat baths. The dissipative structure is driven by an entropic operator, the so…
We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that…
We discuss Hilbert space-valued stochastic differential equations associated with the heat semi-groups of the standard model of non-relativistic quantum electrodynamics and of corresponding fiber Hamiltonians for translation invariant…
Based on Koopman formalism for classical statistical mechanics, we propose a formalism to define hybrid quantum-classical dynamical systems by defining (outer) automorphisms of the C*-algebra of hybrid operators and realizing them as linear…
Recent developments in gravitational path integrals indicate that the nonperturbative physical Hilbert space of a closed universe is one-dimensional within each superselection sector. This raises a basic puzzle: how can a unique…
Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the $F^{th}$ power of a conserved charge: $H=Q^F$ with $F=2,3,...\,.$ This construction, called fractional supersymmetric quantum mechanics, was…
We prove that the solution of certain linear stochastic differential equations in Hilbert spaces, namely those with bounded operators as well as the conservative stochastic Schr\"odinger equations, can be obtained - along the lines of the…
Let $S \subset \mathbb{Z}^{d}$ be a finitely generated subsemigroup. Let $E$ be a product system over $S$. We show that there exists an infinite dimensional separable Hilbert space $\mathcal{H}$ and a semigroup $\alpha:=\{\alpha_x\}_{x \in…
We attempt to reconstruct the irreducible unitary representations of the Banach Lie group $U_0(\H)$ of all unitary operators $U$ on a separable Hilbert space $\H$ for which $U-{\mathbb I}$ is compact, originally found by Kirillov and…
A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…
This paper is concerned with a class of open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices pertaining to finite-level systems. The system interacts with external bosonic fields,…