Statistical Mechanics Lecture Notes 3 - Quantum statistics
... The passage to the statistical mechanics of systems identical quantum particles is achieved in two steps. First step is the appearance of the quantum states. These are generally obtained from stationary or time dependent equations that controls the dynamics of the quantum state. For example, in the ...
... The passage to the statistical mechanics of systems identical quantum particles is achieved in two steps. First step is the appearance of the quantum states. These are generally obtained from stationary or time dependent equations that controls the dynamics of the quantum state. For example, in the ...
RESEARCH STATEMENT I had my training in theoretical physics
... a ferromagnetic phase transition in the thermodynamic limit [3]; viceversa nanosystems with a ferromagnetic phase transition in the thermodynamic limit, might not show ferromagnetic behavior due to finite size fluctuations. Recently we analyzed an ergodicity breaking energy threshold in anisotropic ...
... a ferromagnetic phase transition in the thermodynamic limit [3]; viceversa nanosystems with a ferromagnetic phase transition in the thermodynamic limit, might not show ferromagnetic behavior due to finite size fluctuations. Recently we analyzed an ergodicity breaking energy threshold in anisotropic ...
The Unruh effect revisited
... equidistant at all times, as seen from either of their instantaneous restframes. Below, we will consider a detector moving with acceleration a ...
... equidistant at all times, as seen from either of their instantaneous restframes. Below, we will consider a detector moving with acceleration a ...
Exam I, vers
... (e) None of these: either the field is zero, or it points in some other direction. ...
... (e) None of these: either the field is zero, or it points in some other direction. ...
Carrier density independent scattering rate in
... liquid, i.e. n = 2. In systems with T-linear behavior, such as the cuprates, E in Eq. (4) becomes irrelevant as can be seen by setting n = 1. Furthermore, B ~ 140,41. This has sometimes been attributed to an underlying quantum critical point that causes the relaxation time to become independent of ...
... liquid, i.e. n = 2. In systems with T-linear behavior, such as the cuprates, E in Eq. (4) becomes irrelevant as can be seen by setting n = 1. Furthermore, B ~ 140,41. This has sometimes been attributed to an underlying quantum critical point that causes the relaxation time to become independent of ...
The contents of this module were developed under grant award
... field, something new happens. The spectral lines are SPLIT! In order to explain these observations we introduce another quantum number number, l, which is called the azimuthal quantum number or the angular momentum quantum number. For all atoms with more than one electron the spectral lines are spli ...
... field, something new happens. The spectral lines are SPLIT! In order to explain these observations we introduce another quantum number number, l, which is called the azimuthal quantum number or the angular momentum quantum number. For all atoms with more than one electron the spectral lines are spli ...
Canonical Quantum Gravity as a Gauge Theory with Constraints
... One of the consequences of canonical quantum gravity, which we will not have time to cover, is the extraordinary result that spacetime has a granular, or discrete, structure at very short length scales (≈ 10−35 metres). In this way, we resolve the problem of ultraviolet divergences by depriving them ...
... One of the consequences of canonical quantum gravity, which we will not have time to cover, is the extraordinary result that spacetime has a granular, or discrete, structure at very short length scales (≈ 10−35 metres). In this way, we resolve the problem of ultraviolet divergences by depriving them ...
Erwin Schroedinger gained inspiration
... Light from the sun and from stars was a continuous spectrum – the light ran all the way from red light of long wavelength to violet light with a short wavelength. Actually this was one of Newton’s discoveries, but he used a simple prism. Later sophisticated spectroscopes were developed which allowed ...
... Light from the sun and from stars was a continuous spectrum – the light ran all the way from red light of long wavelength to violet light with a short wavelength. Actually this was one of Newton’s discoveries, but he used a simple prism. Later sophisticated spectroscopes were developed which allowed ...
Michelson-Morley Experiments Revisited and the Cosmic
... below, k = n(n 2 − 1) where n is the dielectric constant of the gas in which the interferometer operates and this gives k = 0 only for the vacuum (n = 1) mode. When operating in gas the Newtonian k value is different from k = 1, namely k = n3 , as we shall see. We show here that interferometer exper ...
... below, k = n(n 2 − 1) where n is the dielectric constant of the gas in which the interferometer operates and this gives k = 0 only for the vacuum (n = 1) mode. When operating in gas the Newtonian k value is different from k = 1, namely k = n3 , as we shall see. We show here that interferometer exper ...
matter, mass and electromagnetic mass
... (Jammer, 2000, pp. 35, 36) These conjectures may be regarded “as the first fieldtheoretic treatment of elementary particles.” (Id., p. 35; see Chapter 34) In 1901, Kaufmann began experiments to measure the inertia and the mass of electrons that were theoretically moving at speeds near to that of lig ...
... (Jammer, 2000, pp. 35, 36) These conjectures may be regarded “as the first fieldtheoretic treatment of elementary particles.” (Id., p. 35; see Chapter 34) In 1901, Kaufmann began experiments to measure the inertia and the mass of electrons that were theoretically moving at speeds near to that of lig ...
Renormalization
In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities.Renormalization specifies relationships between parameters in the theory when the parameters describing large distance scales differ from the parameters describing small distances. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in infinities. When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, this continuum limit, the removal of the ""construction scaffolding"" of lattices at various scales, has to be taken carefully, as detailed below.Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through ""effective"" descriptions. All scales are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each.