Related papers: Quantum Bi-Hamiltonian systems, alternative Hermit…

Recent years have seen significant advances, both theoretical and experimental, in our understanding of quantum many-body dynamics. Given this problem's high complexity, it is surprising that a substantial amount of this progress can be…

For numerous applications of quantum theory it is desirable to be able to apply arbitrary unitary operations on a given quantum system. However, in particular situations only a subset of unitary operations is easily accessible. This raises…

An effective Hamiltonian describing interaction between generic "fast" and a "slow" systems is obtained in the strong interaction limit. The result is applied for studying the effect of quantum phase transition as a bifurcation of the…

The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems, that are those systems which sub-systems are out of consideration. Taking sub-systems into account,…

We explore the relation between quantum geometry in non-Hermitian systems and physically measurable phenomena. We highlight various situations in which the behavior of a non-Hermitian system is best understood in terms of quantum geometry,…

Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in…

Starting from arbitrary Hilbert spaces, we reduce the problem to verify entanglement of any bipartite quantum state to finite dimensional subspaces. Hence, entanglement is a finite dimensional property. A generalization for multipartite…

We revisit qubit-qutrit quantum systems under collective dephasing and answer some of the questions which have not been asked and addressed so far in the literature. In particular, we examine the possibilities of non-trivial phenomena of…

The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the…

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit…

We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…

We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on physical systems in quaternionic quantum theory can be simulated by usual quantum…

Standard quantum mechanics predicts the non-conservation of state norms and probability when the fundamental requirement of the Hermiticity of the Hamiltonian is relaxed. Biorthogonal quantum mechanics, or the more general metric formalism,…

Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…

We analyze the quantization of dynamical systems that do not involve any background notion of space and time. We give a set of conditions for the introduction of an intrinsic time in quantum mechanics. We show that these conditions are a…

A system of a quantum harmonic oscillator bi-linearly coupled with a Glauber amplifier is analysed considering a time-dependent Hamiltonian model. The Hilbert space of this system may be exactly subdivided into invariant finite dimensional…

While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…

This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…

We show the existence of a noncommutative spacetime structure in the context of a complete discussion on the underlying spacetime symmetries for the physical system of a free massless relativistic particle. The above spacetime symmetry…

Dissipative quantum systems are sometimes phenomenologically described in terms of a non-hermitian hamiltonian $H$, with different left and right eigenvectors forming a bi-orthogonal basis. It is shown that the dynamics of waves in open…