相关论文: The non-adiabatic classical geometric phase and it…

Nonadiabatic geometric phases are only dependent on the evolution path of a quantum system but independent of the evolution details, and therefore quantum computation based on nonadiabatic geometric phases is robust against control errors.…

We calculate the geometric phase of a spin-1/2 system driven by a one and two mode quantum field subject to decoherence. Using the quantum jump approach, we show that the corrections to the phase in the no-jump trajectory are different when…

The conception of the conformal phase transition (CPT), which is relevant for the description of non-perturbative dynamics in gauge theories, is discussed.

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions…

Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed…

The aim of this paper is to bridge noncommutative geometry with classical harmonic analysis on Banach spaces, focusing primarily on both classical and noncommutative $\mathrm{L}^p$ spaces. Introducing a notion of Banach Fredholm module, we…

A new geometric framework is developed to describe non-conservative classical field theories, which is based on multisymplectic and contact geometries. Assuming certain additional conditions and using the forms that define this multicontact…

Basic notions of Dirac theory of constrained systems have their analogs in differential geometry. Combination of the two approaches gives more clear understanding of both classical and quantum mechanics, when we deal with a model with…

In the past decades, topological concepts have emerged to classify matter states beyond the Ginzburg-Landau symmetry breaking paradigm. The underlying global invariants are usually characterized by integers, such as Chern or winding…

The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…

We place the representation variety in the broader context of abelian and nonabelian cohomology. We outline the equivalent constructions of the moduli spaces of flat bundles, of smooth integrable connections, and of holomorphic integrable…

In this paper we study the holomorphic bundles over a noncommutative complex torus. We define a noncommutative abelian variety as a kind of deformation of abelian variety and we show that for a restricted deformation parameter, one can…

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one and is in harmony with the modern trends in theoretical physics and potentially admits new…

In a recent letter [Phy. Rev. Lett. 95, 080502 (2005)], it is claimed that based on a new kind of quantum mechanical phase of wave function which is neither dynamical nor geometrical a new kind of phase gate for quantum computation is…

Starting from a simple mapping of a generator of local stochastic dynamics to a quantum Hamiltonian, we derive a condition, which allows us to use the quasi-adiabatic evolution and so relate gapped quantum phases with non-equilibrium's.…

We present three statistical descriptions for systems of classical particles and consider their extension to hybrid quantum-classical systems. The classical descriptions are ensembles on configuration space, ensembles on phase space, and a…

In this work we study the noncommutative nonrelativistic quantum dynamics of a neutral particle, that possesses permanent magnetic and electric dipole momenta, in the presence of an electric and magnetic fields. We use the Foldy-Wouthuysen…

Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…

A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the…

Positive-energy solutions of the Klein-Gordon equation form a Hilbert space of holomorphic functions on the future tube. This domain is interpreted as an extended phase space for the associated classical particle, the extra dimensions being…