Related papers: Interferometric Geometric Phases of $\mathcal{PT}$…
A model in statistical mechanics, characterised by the corresponding Gibbs measure, is a subset of the totality of probability distributions on the phase space. The shape of this subset, i.e., the geometry, then plays an important role in…
We report on recent results showing that the geometric phase can be used as a tool in the analysis of many different physical systems, as mixed boson systems, CPT and CP violations, Unruh effects and thermal states. We show that the…
For time-periodical quantum systems generalized Floquet operator is found to be integral of motion.Spectrum of this invariant is shown to be quasienergy spectrum.Analogs of invariant Floquet operators are found for nonperiodical systems…
$\mathcal{PT}$-symmetric quantum mechanics has been considered an important theoretical framework for understanding physical phenomena in $\mathcal{PT}$-symmetric systems, with a number of $\mathcal{PT}$-symmetry related applications. This…
We propose a novel proposal for geometric quantum gates using three- or two-level systems, in which a controllable variable, the detuning between the driving frequency and the atomic energy spacing, is introduced to realize geometric…
We propose an experimentally feasible scheme to achieve quantum computation based on a pair of orthogonal cyclic states. In this scheme, quantum gates can be implemented based on the total phase accumulated in cyclic evolutions. In…
We generalize the notion of relative phase to completely positive maps with known unitary representation, based on interferometry. Parallel transport conditions that define the geometric phase for such maps are introduced. The interference…
The level crossing problem and associated geometric terms are neatly formulated by the second quantized formulation. This formulation exhibits a hidden local gauge symmetry related to the arbitrariness of the phase choice of the complete…
Following a key idea of unconventional geometric quantum computation developed earlier [Phys. Rev. Lett. 91, 197902 (2003)], here we propose a more general scheme in such an intriguing way: $\gamma_{d}=\alpha_{g}+\eta \gamma _{g}$, where…
We report a phase transition in the projected ensemble - the collection of post-measurement wavefunctions of a local subsystem obtained by measuring its complement. The transition emerges in systems undergoing random permutation dynamics, a…
In this thesis we provide a uniform treatment of two non-adiabatic geometric phases for dynamical systems of mixed quantum states, namely those of Uhlmann and of Sj\"{o}qvist et al. We develop a holonomy theory for the latter which we also…
One of the major open problems in theoretical physics is a consistent quantum gravity theory.Recent developments in thermodynamic phase transitions ofblack holes and their van der Waals-like behavior may provide an interesting quantum…
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 show that sharply defined topological quantum phase transitions are not limited to states of matter with gapped electronic spectra. Such transitions may also occur between two gapless metallic states both with extended Fermi surfaces.…
The geometric phase stands as a foundational concept in quantum physics, revealing deep connections between geometric structures and quantum dynamical evolution. Unlike dynamical phases, geometric phases exhibit intrinsic resilience to…
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
In this article, we use geometric optimal control to completely solve the problem of minimum-time transitions between thermal equilibrium states of the quantum parametric oscillator, which finds applications in various physical contexts. We…
PT-symmetric quantum mechanics is an alternative formulation of quantum mechanics in which the mathematical axiom of Hermiticity (transpose and complex conjugate) is replaced by the physically transparent condition of space-time reflection…
We have analysed here the role of the geometric phase in dynamical mechanism of quantum phase transition in the transverse Ising model. We have investigated the system when it is driven at a fixed rate characterized by a quench time…
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…