This course presents an introduction to statistical mechanics geared towards materials scientists. The concepts of macroscopic thermodynamics will be related to a microscopic picture and a statistical
Introduction to the path integral formulation of quantum mechanics. Derivation of the perturbation expansion of Green's functions in terms of Feynman diagrams. Several applications will be presented,
We study the statistical mechanics and the equilibrium dynamics of a system of classical Heisenberg spins with frustrated interactions on a d -dimensional simple hypercubic lattice, in the limit of infinite dimensionality d -> infinity . In the analysis we ...
This course provides a rigorous introduction to the ideas, methods and results of classical statistical mechanics, with an emphasis on presenting the central tools for the probabilistic description of
Schizophrenia is a complex and devastating mental disorder that influences how one behaves, feels, and thinks. It affects a little less than 1 % of the world population and it is understood to be partly genetically mediated. Several genetic risk factors of ...
Predicting the thermal conductivity of glasses from first principles has hitherto been a very complex problem. The established Allen-Feldman and Green-Kubo approaches employ approximations with limited validity-the former neglects anharmonicity, the latter ...
Recent findings identified electroencephalography (EEG) microstates as the electrophysiological correlates of fMRI resting-state networks. Microstates are defined as short periods (100 ms) during which the EEG scalp topography remains quasi-stable; that is ...
Schizophrenia is a complex psychiatric disorder and many of the factors contributing to its pathogenesis are poorly understood. In addition, identifying reliable neurophysiological markers would improve diagnosis and early identification of this disease. T ...
In statistical mechanics, a microstate is a specific configuration of a system that describes the precise positions and momenta of all the individual particles or components that make up the system. Each microstate has a certain probability of occurring during the course of the system's thermal fluctuations. In contrast, the macrostate of a system refers to its macroscopic properties, such as its temperature, pressure, volume and density.
In statistical mechanics, the grand canonical ensemble (also known as the macrocanonical ensemble) is the statistical ensemble that is used to represent the possible states of a mechanical system of particles that are in thermodynamic equilibrium (thermal and chemical) with a reservoir. The system is said to be open in the sense that the system can exchange energy and particles with a reservoir, so that various possible states of the system can differ in both their total energy and total number of particles.
In statistical thermodynamics, thermodynamic beta, also known as coldness, is the reciprocal of the thermodynamic temperature of a system: (where T is the temperature and kB is Boltzmann constant). It was originally introduced in 1971 (as Kältefunktion "coldness function") by de, one of the proponents of the rational thermodynamics school of thought, based on earlier proposals for a "reciprocal temperature" function. Thermodynamic beta has units reciprocal to that of energy (in SI units, reciprocal joules, ).
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied on various reference points and thermometric substances for definition. The most common scales are the Celsius scale with the unit symbol °C (formerly called centigrade), the Fahrenheit scale (°F), and the Kelvin scale (K), the latter being used predominantly for scientific purposes.
In physics, specifically statistical mechanics, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies (sometimes infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in. In other words, a statistical ensemble is a set of systems of particles used in statistical mechanics to describe a single system. The concept of an ensemble was introduced by J. Willard Gibbs in 1902.
A microstate or ministate is a sovereign state having a very small population or land area, usually both. However, the meanings of "state" and "very small" are not well-defined in international law. Some recent attempts to define microstates have focused on identifying qualitative features that are linked to their size and population, such as partial delegation of their sovereignty to larger states, such as for international defense. Commonly accepted examples of microstates include Andorra, Liechtenstein, Monaco, Nauru, Palau, San Marino and Tuvalu.
The European microstates or European ministates are a set of very small sovereign states in Europe. In modern contexts the term is typically used to refer to the six smallest states in Europe by area: Andorra, Liechtenstein, Malta, Monaco, San Marino, and Vatican City (the Holy See). Four of these states are monarchies, three principalities—Andorra, Liechtenstein, and Monaco—and one papacy, Vatican City. These states trace their status back to the first millennium or the early second millennium except for Liechtenstein, created in the 17th century.
