Related papers: Second quantized formulation of geometric phases
We discuss adiabatic quantum phenomena at a level crossing. Given a path in the parameter space which passes through a degeneracy point, we find a criterion which determines whether the adiabaticity condition can be satisfied. For paths…
Within the frame of a Group Approach to Quantization anomalies arise in a quite natural way. We present in this talk an analysis of the basic obstructions that can be found when we try to translate symmetries of the Newton equations to the…
We find the geometric phase of a two-level system undergoing pure dephasing via interaction with an arbitrary environment, taking into account the effect of the initial system-environment correlations. We use our formalism to calculate the…
This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and…
We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to…
In topological phases in $2+1$ dimensions, anyons fall into representations of quantum group symmetries. As proposed in our work (arXiv:1308.4673), physics of a symmetry enriched phase can be extracted by the Mathematics of (hidden) quantum…
We derive the general form of the non-trivial geometric phase resulting from the unique combination of point group and time reversal symmetries. This phase arises e.g. when a magnetic adatom is adsorbed on a non-magnetic C$_n$ crystal…
The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…
We show that the geometric phase between any two states, including orthogonal states, can be computed and measured using the notion of projective measurement, and we show that a topological number can be extracted in the geometric phase…
Various phenomena related to geometric phases in quantum mechanics are reviewed and explained by analyzing some examples.The concepts of 'parallelism' ,'connections' and 'curvatures' are applied to Aharonov-Bohm (AB) effect, to U(1)phase…
The method of group quantization described in the preceeding paper I is extended so that it becomes applicable to some parametrized systems that do not admit a global transversal surface. A simple completely solvable toy system is studied…
An 't Hooft anomaly is the obstruction for gauging symmetries, and it constrains possible low-energy behaviors of quantum field theories by excluding trivial infrared theories. Global inconsistency condition is recently proposed as a milder…
Based on a generic quantum open system model, we study the geometric nature of decoherence by defining a complex-valued geometric phase through stochastic pure states describing non-unitary, non-cyclic and non-adiabatic evolutions. The…
By viewing entanglement as a state function, a new kind of phase transition takes place: the geometric phase transition. This phenomenon occurs due to singularities in the shape of the entangled states set. It is shown how this result can…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…
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…
We study characteristic aspects of the geometric phase which is associated with the generalized coherent states. This is determined by special orbits in the parameter space defining the coherent state, which is obtained as a solution of the…
We have constructed the geometric phases emerging from the non-trivial topology of a space-dependent magnetic field, interacting with the spin magnetic moment of a neutral particle. Our basic tool is the local unitary transformation which…
A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…