Related papers: Generalised Geometric Phase
A wave packet of a charged particle always make cyclic circular motion in a uniform magnetic field, just like a classical particle. The nonadiabatic geometric phase for an arbitrary wave packet can be expressed in terms of the mean value of…
A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…
The Landau paradigm is a central dogma for understanding phase and phase transitions in condensed matter systems, yet for decades it has been known that a variety of quantum phases exist beyond the framework. Is there a more general…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
We illustrate how geometric gauge forces and topological phase effects emerge in quantum systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices…
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…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases,…
The level crossing problem and associated geometric terms are neatly formulated by using the second quantization technique both in the operator and path integral formulations. The analysis of geometric phases is then reduced to the familiar…
We discuss the presence of a geometrical phase in the evolution of a qubit state and its gauge structure. The time evolution operator is found to be the free energy operator, rather than the Hamiltonian operator.
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…
We propose a class of generalizations of the geometric entanglement for pure states by exploiting the matrix product state formalism. This generalization is completely divested from the notion of separability and can be freely tuned as a…
The optical theorem is a fundamental aspect of quantum scattering theory. Here, we generalize this theorem to the case where the incident scattering state is a superposition of internal states of the collision partners, introducing…
We use so-called geometrical approach in description of transition from regular motion to chaotic in Hamiltonian systems with potential energy surface that has several local minima. Distinctive feature of such systems is coexistence of…
In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…
The quantum completion of the space of connections in a manifold can be seen as the set of all morphisms from the groupoid of the edges of the manifold to the (compact) gauge group. This algebraic construction generalizes the analogous…
Geometric phase plays an important role in evolution of pure or mixed quantum states. However, when a system undergoes decoherence the development of geometric phase may be inhibited. Here, we show that when a quantum system interacts with…
The adiabatic theorem states that when the time evolution of the Hamiltonian is "infinitely slow", a system, when started in the ground state, remains in the instantaneous ground state at all times. This, however, does not mean that the…
The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic time-periodic parameters are discussed in the framework of squeezed state. It is shown that the cyclic and quasicyclic squeezed states…
In this paper I introduce the idea of geometrogenesis as suggested in the group field theory literature and I offer a criticism of it. Geometrogenesis in the context of GFT is the idea that what we observe as the big bang is nothing else…