Related papers: Reflection positivity and quantum Griffiths' inequ…
An input-output model of a two-level quantum system in the Heisenberg picture is of bilinear form with constant system matrices, which allows the introduction of the concepts of controllability and observability in analogy with those of…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
A strongly correlated electron system associated with the quantum superalgebra ${U}_q[{osp}(2|2)]$ is studied in the framework of the quantum inverse scattering method. By solving the graded reflection equation, two classes of…
We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of…
The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the $\alpha$ (the…
The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. In this paper we focus on nonlinear electronic transport through an interacting…
The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinates [x^{i},x^{j}]=\omega^{ij}(x), and construct the complete algebra of…
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
The functional Schrodinger equation is used to study the quantum collapse of a gravitating, spherical domain wall and a massless scalar field coupled to the metric. The approach includes backreaction of pre-Hawking radiation on the…
We consider hamiltonian models representing an arbitrary number of spin $1/2$ fermion quantum fields interacting through arbitrary processes of creation or annihilation of particles. The fields may be massive or massless. The interaction…
We employ the influence functional technique to trace out the photonic contribution from full quantum electrodynamics. The reduced density matrix propagator for the spinor field is then constructed. We discuss the role of time-dependent…
Coherent subspaces spanned by a finite number of coherent states are introduced, in a quantum system with Hilbert space that has odd prime dimension $d$. The set of all coherent subspaces is partitioned into equivalence classes, with $d^2$…
Inspired by the theory of apartness relations of Scott, we establish a positive theory of dissimilarity valued in an involutive quantale $\mathsf{Q}$ without the aid of negation. It is demonstrated that a set equipped with a…
Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…
The equilibrium dynamics of the spin-1/2 XX chain is re-examined within a recently developed formalism based on the quantum transfer matrix and a thermal form factor expansion. The transversal correlation function is evaluated in real time…
In previous investigations of the Two-Rotor Model with axially symmetric rotors the wave functions were assumed to be invariant under inversion of the axes of the rotors, which restricted the spectrum to positive parity states. We relax…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
The quantum rotor represents, after the harmonic oscillator, the next obvious quantum system to study the complementary pair of variables: the angular momentum and the unitary shift operator in angular momentum. Proper quantification of…
Quantum mechanics violates Leggett-Garg inequalities because the operator formalism predicts correlations between different spin components that would correspond to negative joint probabilities for the outcomes of joint measurements.…
In this paper we propose a time-independent \textit{equality} and time-dependent \textit{inequality}, suitable for an experimental test of the hypothesis of realism. The derivation of these relations is based on the concept of conditional…