# Bogoliubov's Vision: Quasiaverages and Broken Symmetry to Quantum Protectorate and Emergence

@article{Kuzemsky2010BogoliubovsVQ, title={Bogoliubov's Vision: Quasiaverages and Broken Symmetry to Quantum Protectorate and Emergence}, author={Alexander L. Kuzemsky}, journal={arXiv: Statistical Mechanics}, year={2010} }

In the present interdisciplinary review we focus on the applications of the symmetry principles to quantum and statistical physics in connection with some other branches of science. The profound and innovative idea of quasiaverages formulated by N.N. Bogoliubov, gives the so-called macro-objectivation of the degeneracy in domain of quantum statistical mechanics, quantum field theory and in the quantum physics in general. We discuss the complementary unifying ideas of modern physics, namely…

## Figures from this paper

## 30 Citations

### Fundamental principles of theoretical physics and concepts of quasiaverages, quantum protectorate and emergence

- Physics
- 2013

In the present paper we discuss the interrelation of the advanced interdisciplinary concepts of modern physics such as symmetry breaking, quantum protectorate, emergence and the Bogoliubov’s concept…

### Fundamental Principles of Theoretical Physics and Concepts of Quantum Protectorate and Emergence

- Physics, Education
- 2012

A concise survey of the advanced unifying ideas of modern physics, namely, spontaneous symmetry breaking, quasiaverages, quantum protectorate and emergence was presented. The interrelation of the…

### Bogoliubov's Foresight and Development of the Modern Theoretical Physics

- Physics
- 2011

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…

### Bogoliubov's Vision and Modern Theoretical Physics

- Physics
- 2010

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…

### Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems

- Physics
- 2015

The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the…

### In Search of Time Lost: Asymmetry of Time and Irreversibility in Natural Processes

- Physics
- 2020

In this survey, we discuss and analyze foundational issues of the problem of time and its asymmetry from a unified standpoint. Our aim is to discuss concisely the current theories and underlying…

### Irreversible Evolution of Open Systems and the Nonequilibrium Statistical Operator Method

- Physics
- 2019

The effective approach to the foundation of the nonequilibrium statistical mechanics on the basis of dynamics was formulated by Bogoliubov in his seminal works. His ideas of reduced description were…

### Physical limitations of the Hohenberg–Mermin–Wagner theorem

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2021

The Hohenberg–Mermin–Wagner (HMW) theorem states that infrared (IR) fluctuations prevent long-range order which breaks continuous symmetries in two dimensions (2D), at finite temperatures. We note…

### Another operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivity

- PhysicsScientific reports
- 2022

In the preceding papers, imposing certain complicated and strong conditions, the present author showed that the solution to the BCS-Bogoliubov gap equation in superconductivity is twice…

### An operator-theoretical study on the BCS-Bogoliubov model of superconductivity near absolute zero temperature

- PhysicsScientific reports
- 2021

The behavior near absolute zero temperature of the thus-obtained entropy, the specific heat, the solution and the critical magnetic field is shown from the viewpoint of operator theory since the present author did not study it in the preceding papers.

## References

SHOWING 1-10 OF 427 REFERENCES

### Quantum Dynamics in the Thermodynamic Limit.

- Physics
- 2008

The description of spontaneous symmetry breaking that underlies the connection between classically ordered objects in the thermodynamic limit and their individual quantum-mechanical building blocks…

### Statistical Mechanics and the Physics of Many-Particle Model Systems

- Physics
- 2011

The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic…

### Symmetry breaking in Heisenberg antiferromagnets

- Mathematics, Physics
- 1993

We extend Griffith's theorem on symmetry breaking in quantum spin systems to the situation where the order operator and the Hamiltonian do not commute with each other. The theorem establishes that…

### Magnons in a model with antiferromagnetic properties

- Physics
- 1969

SummaryThe symmetry properties of the photon are different from those expected at first sight for a Goldstone particle belonging to a degeneracy of the ground state with respect to the isospin group.…

### Theory of Superfluidity

- Physics
- 1979

We propose a new description of superfluidity based upon the fact t hat Bogoliubov¹s theory of superfluidity e xhibits some so far unsuspected macroscopic quantum waves (MQws), which have a…

### Quasi-Particles and Gauge Invariance in the Theory of Superconductivity

- Physics
- 2011

Ideas and techniques known in quantum electrodynamics have been applied to the Bardeen-Cooper-Schrieffer theory of superconductivity. In an approximation which corresponds to a generalization of the…

### Spontaneous symmetry breaking as a basis of particle mass

- Physics
- 2007

Electroweak theory joins electromagnetism with the weak force in a single quantum field theory, ascribing the two fundamental interactions—so different in their manifestations—to a common symmetry…

### Course 2: The Quantum Hall Effect: Novel Excitations and Broken Symmetries

- Physics
- 1999

The Quantum Hall Effect (QHE) is one of the most remarkable condensed-matter phenomena discovered in the second half of the 20th century. It rivals superconductivity in its fundamental significance…

### Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance

- Physics
- 2005

We define for quantum many-body systems a quasiadiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density…

### Boulevard of Broken Symmetries

- Physics
- 1998

Effective theories of quantum liquids (superconductors and superfluids of various types) are derived starting from microscopic models at the absolute zero of temperature. Special care is taken to…