相关论文: The non-adiabatic classical geometric phase and it…
Based on the classical and quantum ergodic hierarchy, a framework for mixed systems with a phase space composed by two uncorrelated integrable and chaotic regions is presented. It provides some features of mixed systems connecting the…
The fate of the molecular geometric phase in an exact dynamical framework is investigated with the help of the exact factorization of the wavefunction and a recently proposed quantum hydrodynamical description of its dynamics. An…
We present how the formalism of geometric phases in adiabatic quantum dynamics provides geometric realisations permitting to ``embody'' the Everett's many-worlds interpretation of quantum mechanics, including interferences between the…
In this work it is shown that there is an inherent nonlinear evolution in the dynamics of the so-called generalized coherent states. To show this, the immersion of a classical manifold into the Hilbert space of quantum mechanics is…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…
We propose a theoretical framework that captures the geometric vector potential emerging from the non-adiabatic spin dynamics of itinerant carriers subject to arbitrary magnetic textures. Our approach results in a series of constraints on…
An attempt is made to extend some of the basic paradigms of dynamics, from the viewpoint of (continuous) flows, to non-metric manifolds.
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
An algebraic framework for noncommutative bundles with (quantum) homogeneous fibres is proposed. The framework relies on the use of principal coalgebra extensions which play the role of principal bundles in noncommutative geometry which…
This paper applies the formalism of classical, Gibbs-Boltzmann statistical mechanics to the phenomenon of non-thermal damage. As an example, a non-thermal fiber-bundle model with the global uniform (meanfield) load sharing is considered.…
It is shown that any second order dynamic equation on a configuration bundle $Q\to R$ of non-relativistic mechanics is equivalent to a geodesic equation with respect to a (non-linear) connection on the tangent bundle $TQ\to Q$. The case of…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
We propose a general scheme for the "logic" of elementary propositions of physical systems, encompassing both classical and quantum cases, in the framework given by Non Commutative Geometry. It involves Baire*-algebras, the non-commutative…
The non-Hermitian Schr\"odinger equation is re-expressed generally in the form of Hamilton's canonical equation without any approximation. Its quantization called non-Hermitian quantum field theory is discussed. By virtue of the canonical…
Using Grassmann variant of classical mechanics, we construct Lagrangian dynamics of classical spinning particle in (possibly non-abelian) gauge fields. Quantization of this model is briefly discussed.
The existence of Hopf fibrations S^{2N+1}/S^1 = CP^N and S^{4K+3}/S^3 = HP^K allows us to treat the Hilbert space of generic finite-dimensional quantum systems as the total bundle space with respectively $U(1)$ and $SU(2)$ fibers and…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…
\noindent We briefly discuss some algebraic and geometric aspects of the generalized Poisson bracket and non--commutative phase space for generalized quantum dynamics, which are analogous to properties of the classical Poisson bracket and…
The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would…