Geometric Phases
英文摘要：
The differential geometric aspects of Geometric Phases are reviewed.
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Differential Geometry of Quantum States, Observables and Evolution
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the relevant geometrical structures and their associated algebraic properties are highlighted, and the Qubit example is thoroughly discussed.
math-phmath.MP
Some geometric features of Berry's phase
In this letter, we elaborate on the identification and construction of the differential geometric elements underlying Berry's phase. Berry bundles are built generally from the physical data of the quantum system under study. We apply this construction to typical and recently investigated systems presenting Berry's phase to explore their geometric features.
math-phmath.MPquant-ph
Operational geometric phase for mixed quantum states
Geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper we introduce an operational geometric phase for mixed quantum states, based on spectral weighted traces of holonomies, and we prove that it generalizes the standard definition of geometric phase for mixed states, which is based on quantum interferometry. We also introduce higher order geometric phases, and prove that under a fairly weak, generically satisfied, requirement, there is always a well-defined geometric phase of some order. …
math-phmath.MPquant-ph
On the geometric phase for Gaussian states
We show the explicit expression of the geometric phase for $n$-partite Gaussian states. In our analysis, the covariance matrix can be obtained as a boundary term of the geometric phase.
cond-mat.othermath-phmath.MP
Geometric phases and quantum phase transitions in open systems
The relationship between quantum phase transition and complex geometric phase for open quantum system governed by the non-Hermitian effective Hamiltonian with the accidental crossing of the eigenvalues is established. In particular, the geometric phase associated with the ground state of the one-dimensional dissipative Ising model in a transverse magnetic field is evaluated, and it is demonstrated that related quantum phase transition is of the first order.
hep-thmath-phmath.MP
Smooth Loops, Generalized Coherent States and Geometric Phases
A description of generalized coherent states and geometric phases in the light of the general theory of smooth loops is given.
hep-thmath-phmath.MP
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Geometric phases in quantum control disturbed by classical stochastic processes
We describe the geometric (Berry) phases arising when some quantum systems are driven by control classical parameters but also by outer classical stochastic processes (as for example classical noises). The total geometric phase is then divided into an usual geometric phase associated with the control parameters and a second geometric phase associated with the stochastic processes. The geometric structure in which these geometric phases take place is a composite bundle (and not an usual principal bundle), which is explicitely built in this paper. We explain why the composite bundle structure is…
math-phmath.MP
The non-adiabatic classical geometric phase and its bundle-theoretic interpretation
A bundle theoretic interpretation of the non-adiabatic classical geometric phase is given in the Koopman representation of dynamics
math-phmath.DSmath.MP
Defects and phase transitions to geometric phases of abelian GLSMs
We consider gauged linear sigma models with gauge group U(1) that exhibit a geometric as well as a Landau Ginzburg phase. We construct defects that implement the transport of D-branes from the Landau-Ginzburg phase to the geometric phase. Through their fusion with boundary conditions these defects in particular provide functors between the respective D-brane categories. The latter map (equivariant) matrix factorizations to coherent sheaves and can be formulated explicitly in terms of complexes of matrix factorizations.
hep-thmath-phmath.AG
