Related papers: Interferometric Geometric Phases of $\mathcal{PT}$…
This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition $H^\dagger=H$ on the Hamiltonian, where $\dagger$ represents the mathematical operation of complex conjugation and matrix…
A conventional quantum phase transition (QPT) occurs not only at zero temperature, but also exhibits finite-temperature quantum criticality. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the…
Dynamical phases are obtained for a quantum thermal engine, whose working medium is a single harmonic oscillator. The dynamics of this engine is obtained by using four steps where in two steps the time dependent frequency is changing. In…
The parity-time-reversal- ($\mathcal{PT}$) symmetric quantum mechanics (PTQM) has developed into a noteworthy area of research. However, to date most known studies of PTQM focused on the spectral properties of non-Hermitian Hamiltonian…
The ground states of noninteracting fermions in one-dimension with chiral symmetry form a class of topological band insulators, described by a topological invariant that can be related to the Zak phase. Recently, a generalization of this…
Transitions of many-particle quantum systems between distinct phases at absolute-zero temperature, known as quantum phase transitions, require an exacting treatment of particle correlations. In this work, we present a general…
We study the geometric phase (GP) of a two-level atom coupled to an environment composed of free space and a dielectric nanosphere in thermal and out of thermal equilibrium. We analytically and numerically analyze the optical properties and…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
We propose a new strategy to physically implement a universal set of quantum gates based on geometric phases accumulated in the nondegenerate eigenstates of a designated invariant operator in a periodic physical system. The system is driven…
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…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
Dynamic quantum phase transitions (DQPT) following quantum quenches exhibit singular behavior of the overlap between the initial and evolved states. Here we present a formalism to incorporate a geometric phase into quench dynamics of mixed…
We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase…
Two representations of mixed states by state-vectors, known as purified state and thermal vacuum, have been realized on quantum computers. While the two representations look similar, they differ by a partial transposition in the ancilla…
We investigate the behavior of geometric phase (GP) and geometric entanglement (GE), a multipartite entanglement measure, across quantum phase transitions in Rydberg atom chains. Using density matrix renormalization group calculations and…
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…
Symmetries are important guiding principle for phase transitions. We systematically construct field theory models with local quantum fields that exhibit the following phase transitions: (1) different symmetry protected topological (SPT)…
An equilibrium state can be represented by a pure quantum state, which we call a thermal pure quantum (TPQ) state. We propose a new TPQ state and a simple method of obtaining it. A single realization of the TPQ state suffices for…
We study the phase diagram and finite temperature properties of an integrable generalization of the one-dimensional super-symmetric t-J model containing interactions explicitly breaking parity-time reversal (PT) symmetries. To this purpose,…