Related papers: Detailed analysis of quantum phase transitions wit…
The transition from arbitrary to chaotic fluctuation properties in quantum systems is studied in a random matrix model. It is assumed that the Hamiltonian can be written as the sum of an arbitrary and a chaos producing part. The Gaussian…
Bosonic quantum devices offer a novel approach to realize quantum computations, where the quantum two-level system (qubit) is replaced with the quantum (an)harmonic oscillator (qumode) as the fundamental building block of the quantum…
Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra.
Quantum link models extend lattice gauge theories beyond the traditional Wilson formulation and present promising candidates for both digital and analog quantum simulations. Fermionic matter coupled to $U(1)$ quantum link gauge fields has…
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-dimensional lattice model of SU(2)_{4} anyons containing a transition into the topological ordered phase state is considered. An effective low-energy Hamiltonian is found for half-integer and integer indices of the type of strongly…
The spherical to deformed $\gamma -unstable$ shape- phase transition in odd-A nuclei is investigated by using the Dual algebraic structures and the affine $SU(1,1)$ Lie Algebra within the framework of the interacting boson - fermion model.…
Background: In the last few decades quantum phase transitions have been of great interest in Nuclear Physics. In this context, two-fluid algebraic models are ideal systems to study how the concept of quantum phase transition evolves when…
We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian,…
In most cases, excited state quantum phase transitions can be associated with the existence of critical points (local extrema or saddle points) in a system's classical limit energy functional. However, an excited-state quantum phase…
The study of dynamical phase transitions has been attracting considerable research efforts in the last decade. One theme of present interest is to search for exotic scenarios beyond the framework of equilibrium phase transitions. Here, we…
Quantum phase transitions occur at zero temperature, when the ground state of a Hamiltonian undergoes a qualitative change as a function of a control parameter. We consider a particularly interesting system with competing one-, two- and…
Quadratic bosonic Hamiltonians and their associated unitary transformations form a fundamental class of operations in quantum optics, modelling key processes such as squeezing, displacement, and beam-splitting. Their Heisenberg-picture…
The abstract mathematical structure behind the positive energy quantization of linear classical systems is described. It is separated into 3 stages: the description of a classical system, the algebraic quantization and the Hilbert space…
We investigate a two-parametric family of one-dimensional non-Hermitian complex potentials with parity-time ($\mathcal{PT}$) symmetry. We find that there exist two distinct types of phase transitions, from an unbroken phase (characterized…
In this work we define a formal notion of a quantum phase crossover for certain Bethe ansatz solvable models. The approach we adopt exploits an exact mapping of the spectrum of a many-body integrable system, which admits an exact Bethe…
We consider an ensemble of three-level particles in lambda-configuration interacting with two bosonic modes. The Hamiltonian has the form of a generalized Dicke-model. We show that in the thermodynamic limit this model supports a…
We analyze a system of polar molecules in a one-dimensional optical lattice. By controlling the internal structure of the polar molecules with static electric and microwave fields, we demonstrate the appearance of a quantum phase transition…
We study the ground state phase diagram and the critical properties of interacting Bosons in one dimension by means of a quantum Monte Carlo technique. The direct experimental realization is a chain of Josephson junctions. For finite-range…
Non-Hermitian systems have attracted considerable interest in recent years owing to their unique topological properties that are absent in Hermitian systems. While such properties have been thoroughly characterized in free fermion models,…