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It has been found that complex non-Hermitian quantum-mechanical Hamiltonians may have entirely real spectra and generate unitary time evolution if they possess an unbroken $\cP\cT$ symmetry. A well-studied class of such Hamiltonians is $H=…
Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
Life on earth is distinguished by long-lived correlations in time. The patterns of material organization that characterize living organisms today are contingent on events that occurred billions of years ago. This contingency is a necessary…
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with…
Non hermitian Hamiltonians play an important role in the study of dissipative quantum systems. We show that using states with time dependent normalization can simplify the description of such systems especially in the context of the…
Molecular dynamics simulations use statistical mechanics at the atomistic scale to enable both the elucidation of fundamental mechanisms and the engineering of matter for desired tasks. The behavior of molecular systems at the microscale is…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
Space-time non-commutative theories are non-local in time. We develop the Hamiltonian formalism for non-local field theories in d space-time dimensions by considering auxiliary d+1 dimensional field theories which are local with respect to…
An outline of the basic Riemannian structures underlying the separation of variables in the Hamilton-Jacobi equation of natural Hamiltonian systems.
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-hermitian Hamiltonian H_{eff}, in accord with the Wigner--Weisskopf approximation, and an additional…
The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic quantum theory is investigated. It is shown that the time evolution exhibits three different characteristics, depending on the values of the parameters of the…
We consider a non-Hermitian Hamiltonian in order to effectively describe a two-level system coupled to a generic dissipative environment. The total Hamiltonian of the model is obtained by adding a general anti-Hermitian part, depending on…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…
We re-analyze the quasi-linear self consistent dynamics for the beam-plasma instability, by comparing the theory predictions to numerical simulations of the corresponding Hamiltonian system. While the diffusive features of the asymptotic…
A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…
In a vast class of systems, which includes members as diverse as sedimenting particles and bird flocks, interactions do not stem from a potential, and are in general nonreciprocal. Thus, it is not possible to define a conventional energy…