Moriya, Hajime
Published in
Communications in Mathematical Physics

We discuss fermion grading symmetry for quasi-local systems with graded commutation relations. We introduce a criterion of spontaneously symmetry breaking (SSB) for general quasi-local systems. It is formulated based on the idea that each pair of distinct phases (appeared in spontaneous symmetry breaking) should be disjoint not only for the total s...

Robnik, Marko Romanovski, Valery G.
Published in
Open Systems & Information Dynamics

The theory of adiabatic invariants has a long history, and very important implications and applications in many different branches of physics, classically and quantally, but is rarely founded on rigorous results. Here we treat the general time-dependent one-dimensional harmonic oscillator, whose Newton equation q + ω2(t)q = 0 cannot be solved in ge...

Kajiura, Hiroshige Stasheff, Jim
Published in
Communications in Mathematical Physics

We define a homotopy algebra associated to classical open-closed strings. We call it an open-closed homotopy algebra (OCHA). It is inspired by Zwiebach's open-closed string field theory and also is related to the situation of Kontsevich's deformation quantization. We show that it is actually a homotopy invariant notion; for instance, the minimal mo...

Exner, Pavel Harrell, Evans M. Loss, Michael
Published in
Letters in Mathematical Physics

Alicki, Robert
Published in
Open Systems & Information Dynamics

Using few very general axioms which should be satisfied by any reasonable theory consistent with the Second Law of Thermodynamics we argue that: a) “no-cloning theorem” is meaningful for a very general theoretical scheme including both quantum and classical models, b) in order to describe self-replication, Wigner’s “cloning” process should be repla...

Tadej, Wojciech Życzkowski, Karol
Published in
Open Systems & Information Dynamics

Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent cases known for the dimensions N = 2,..., 16. In particular, we explicitly write down some families of complex...

Khrennikov, Andrei Volovich, Yaroslav
Published in
Open Systems & Information Dynamics

We analyze dynamical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. In particular we study the problem of discrete energy levels of hydrogen atom. We are able to reconstruct potential which in discrete time formalism leads to energy levels of unperturbed hydrogen atom. We also consider linear energy levels...

Graczyk, J. Kozlovski, O.S.
Published in
Communications in Mathematical Physics

There exists a universal constant σ

Horwood, Joshua T. McLenaghan, Raymond G. Smirnov, Roman G.
Published in
Communications in Mathematical Physics

The problem of the invariant classification of the orthogonal coordinate webs defined in Euclidean space is solved within the framework of Felix Klein’s Erlangen Program. The results are applied to the problem of integrability of the Calogero-Moser model.

Lu, Guangcun
Published in
Communications in Mathematical Physics

This paper constructs and studies the Gromov-Witten invariants and their properties for noncompact geometrically bounded symplectic manifolds. Two localization formulas for GW-invariants are also proposed and proved. As applications we get solutions of the generalized string equation and dilation equation and their variants. The more solutions of W...