Related papers: Bogoliubov's Theory: A Paradigm of Quantum Phase T…
We use the Bogoliubov theory of atoms in an optical lattice to study the approach to the Mott-insulator transition. We derive an explicit expression for the superfluid density based on the rigidity of the system under phase variations. This…
Bogoliubov's 1947 approximation, originally developed in the microscopic theory of superfluidity, laid the foundation for solving previously intractable quantum models and later became part of "quantum mathematics". Regarding mathematically…
Our goal will be the description of a theory of Gribov's type as a physical process of phase transition in the context of a spontaneous symmetry breaking. We mainly focus at the quantum stability of the whole process.
We analyse the finite-temperature phase diagram of a dipolar Bose Einstein Condensate confined in a tubular geometry. The effect of thermal fluctuations is accounted for by means of Bogoliubov theory employing the local density…
A brief survey of the author's works on the fundamental conceptual ideas of quantum statistical physics developed by N. N. Bogoliubov and his school was given. The development and applications of the method of quasiaverages to quantum…
The paper advocates the Bogoliubov method of quasi-averages for quantum systems. First, we elucidate its applications to study the phase transitions with Spontaneous Symmetry Breaking (SSB). To this aim we consider example of Bose-Einstein…
We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for \emph{metastable states} in \emph{finite size systems}. In particular, we…
Quantum Cosmology and Gravity are formulated here as the primary and secondary quantizations of the energy constraints by analogy with the historical formulation of quantum field theory. New fact is that both the Universe and its matter are…
We study the quantum phase transition in optical lattices using ordinary Bose Hubbard Hamiltonian within two loop approximation in variational perturbation theory. We have shown that this approximation can reproduce superfluid Mott…
Spin-boson models are essentially useful in the understanding of quantum optics, nuclear physics, quantum dissipation, and quantum computation. We discuss quantum phase transitions in various spin-boson Hamiltonians, compare, and contrast…
Bogoliubov transformations have been successfully applied in several Condensed Matter contexts, e.g., in the theory of superconductors, superfluids, and antiferromagnets. These applications are based on bulk models where translation…
These lecture notes provide a relatively self-contained introduction to field theoretic methods employed in the study of classical and quantum phase transitions.
A unified description of i) classical phase transitions and their remnants in finite systems and ii) quantum phase transitions is presented. The ensuing discussion relies on the interplay between, on the one hand, the thermodynamic concepts…
In this paper, Landau theory for phase transitions is shown to be a useful approach also for quantal system such as atomic nucleus. A detailed analysis of critical exponents of ground state quantum phase transition between and limits of…
This study targets quantum phases which are characterized by topological properties and no associated with the symmetry breaking. We concern ourselves primarily with the transitions among these quantum phases. This type of quantum phase…
We develop a quantum many-body theory of the Bose-Hubbard model based on the canonical quantization of the action derived from a Gutzwiller mean-field ansatz. Our theory is a systematic generalization of the Bogoliubov theory of…
We consider a variational approach to the Bose-Hubbard model based on Bogoliubov theory. We introduce the grand canonical and canonical free energy functionals for which we prove the existence of minimizers. By analyzing their structure we…
In this paper we study the superfluid-Mott-insulator phase transition of ultracold dilute gas of bosonic atoms in an optical lattice by means of Green function method and Bogliubov transformation as well. The superfluid- Mott-insulator…
A suggested amendment to the temperature dependencies in the thermodynamic potential of the Ginzburg-Sobyanin theory of superfluidity, which makes it possible to obtain critical exponents that are consistent with the general relations of…
Metal--insulator transitions and transitions between different quantum Hall liquids are used to describe the physical ideas forming the basis of quantum phase transitions and the methods of application of theoretical results in processing…