Related papers: Interacting and noninteracting integrable systems
Quantum entanglement describes superposition states in multi-dimensional systems, at least two partite, which cannot be factorized and are thus non-separable. Non-separable states exist also in classical theories involving vector spaces. In…
The no-pumping theorem states that seemingly natural driving cycles of stochastic machines fail to generate directed motion. Initially derived for single particle systems, the no-pumping theorem was recently extended to many-particle…
The present paper presents a new general conception of interaction between physical systems, differing significantly from that of both classical physics and quantum physics as generally understood. We believe this conception could provide…
Matter-wave optics is often viewed as a linear analogue of photonics, where noninteracting particles are coherently split, diffracted, and recombined, and interference arises from single-particle coherence. In ultracold quantum gases,…
A large (infinitely-dimensional) class of completely integrable (possibly non-autonomous) spin chains is discovered associated to an infinite-dimensional Lie Algebra of infinite rank. The complete set of integrals of motion is constructed…
The usual formulation of thermodynamics is based on the additivity of macroscopic systems. However, there are numerous examples of macroscopic systems that are not additive, due to the long-range character of the interaction among the…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on…
Interacting particle systems are continuous time Markov processes which are used to construct models in many disciplines. Monotonicity is a property that some interacting particle systems possess. A monotone interacting particle system is…
We discuss the possibility of making the {\it initial} definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical…
We explore conditions on the covariance matrices of a consistent chain of mean zero finite mode Gaussian states in order that the chain may be exchangeable or stationary. For an exchangeable chain our conditions are necessary and…
Using Onsager's variational principle, we derive dynamical equations for a nonequilibrium active system with odd elasticity. The elimination of the extra variable that is coupled to the nonequilibrium driving force leads to the…
We construct a two-class asymmetric interacting particle system with $U_q(so_6)$ or $U_q(so_8)$ symmetry, in which up to two particles may occupy a site if the two particles have different class. The particles exhibit a drift, but there is…
A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be…
We consider general integrable systems on graphs as discrete flat connections with the values in loop groups. We argue that a certain class of graphs is of a special importance in this respect, namely quad-graphs, the cellular…
Onsager's relations allow one to express the second law of thermodynamics in terms of the underlying associated currents. These relations, however, are usually valid only close to equilibrium. Using a quantum phase space formulation of the…
The entanglement properties of quenched quantum systems have been studied for a decade, however results in dimensions other than $d=1$ are generally lacking. We remedy this by investigating the entanglement properties of bosonic critical…
Interactions between many (initially separate) quantum systems raise the question on how to prepare and how to compute the measurable results of their interaction. When one prepares each system individually and let them interact, one has to…
We explicitly construct an integrable and strongly interacting dissipative quantum circuit via a trotterization of the Hubbard model with imaginary interaction strength. To prove integrability, we build an inhomogeneous transfer matrix,…
We analyse the stability of large, linear dynamical systems of variables that interact through a fully connected random matrix and have inhomogeneous growth rates. We show that in the absence of correlations between the coupling strengths,…