Comparison of Theory and Experiment for a One
... Although a number of theoretical analyses related to a one-atom laser have appeared in the literature [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], these prior treatments have not been specific to the parameter range of our recent experiment as reported in Ref. [1]. Because of this circu ...
... Although a number of theoretical analyses related to a one-atom laser have appeared in the literature [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], these prior treatments have not been specific to the parameter range of our recent experiment as reported in Ref. [1]. Because of this circu ...
4 - ckw
... temperature is lowered. Forces of cohesion tend to overcome thermal motion, and atoms rearrange themselves in a more ordered state. Phase changes occur abruptly at some critical temperature although evidence that one will occur can be found on a microscopic scale as the critical temperature is appro ...
... temperature is lowered. Forces of cohesion tend to overcome thermal motion, and atoms rearrange themselves in a more ordered state. Phase changes occur abruptly at some critical temperature although evidence that one will occur can be found on a microscopic scale as the critical temperature is appro ...
4 - ckw
... (on the level of the van der Waals equation) which contains the essential features of the phase transition. We then can use stability arguments to study the phase transition in some detail. Most phase transitions have associated with them a critical point (the liquid- solid transition is one of the ...
... (on the level of the van der Waals equation) which contains the essential features of the phase transition. We then can use stability arguments to study the phase transition in some detail. Most phase transitions have associated with them a critical point (the liquid- solid transition is one of the ...
THE RENORMALIZATION GROUP AND CRITICAL PHENOMENA
... interval L to L+6L. To average over these wavelengths of fluctuations one starts with the Boltzmann factor e -‘I where the wavelengths between L and L+61, are still present in M(x), and then averages over fluctuations in M(x) with wavelengths between L and L+6L. The result of these fluctuation avera ...
... interval L to L+6L. To average over these wavelengths of fluctuations one starts with the Boltzmann factor e -‘I where the wavelengths between L and L+61, are still present in M(x), and then averages over fluctuations in M(x) with wavelengths between L and L+6L. The result of these fluctuation avera ...
Recurrence spectroscopy of atoms in electric fields: Failure of classical
... In this paper we compare quantum and semiclassical calculations for hydrogen at fixed scaled energy in an electric field for different ranges of E and F ~we use F for the electric field strength to avoid confusion with the energy E). Results for m50 and 1 spectra are reported. Quantum calculations a ...
... In this paper we compare quantum and semiclassical calculations for hydrogen at fixed scaled energy in an electric field for different ranges of E and F ~we use F for the electric field strength to avoid confusion with the energy E). Results for m50 and 1 spectra are reported. Quantum calculations a ...
Disorder-induced order with ultra-cold atoms
... the gas particles, and temperature is a direct measure of the thermal motion of the particles [Feynman et al., 1964]. A direct consequence of this description is that temperature is not expressed in an arbitrary scale such as degrees Celsius or Fahrenheit, but rather in the absolute Kelvin scale. Ze ...
... the gas particles, and temperature is a direct measure of the thermal motion of the particles [Feynman et al., 1964]. A direct consequence of this description is that temperature is not expressed in an arbitrary scale such as degrees Celsius or Fahrenheit, but rather in the absolute Kelvin scale. Ze ...
Introduction to Nonequilibrium Quantum Field Theory
... heavy-ion collision experiments, as well as applications in astrophysics and cosmology urge a quantitative understanding of far-from-equilibrium quantum field theory. The initial stages of a heavy-ion collision require considering extreme nonequilibrium dynamics. Connecting this far-from-equilibrium ...
... heavy-ion collision experiments, as well as applications in astrophysics and cosmology urge a quantitative understanding of far-from-equilibrium quantum field theory. The initial stages of a heavy-ion collision require considering extreme nonequilibrium dynamics. Connecting this far-from-equilibrium ...
Theory and simulation of polar and nonpolar polarizable fluids
... molecules that are also polarizable the molecules are modeled as anisotropic Drude oscillators in which the electronic motion along the direction of the permanent dipole and perpendicular to it have different force constants, or equivalently different polarizabilities along the parallel and perpendi ...
... molecules that are also polarizable the molecules are modeled as anisotropic Drude oscillators in which the electronic motion along the direction of the permanent dipole and perpendicular to it have different force constants, or equivalently different polarizabilities along the parallel and perpendi ...
Closed and Open String Theories in Non-Critical Backgrounds
... 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2. Two-dimensional Open String Theory and the FZZT branes . . . . . 52 ...
... 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2. Two-dimensional Open String Theory and the FZZT branes . . . . . 52 ...
ACE Answers Investigation 4
... angle measures because the position of the original figure matters. For the rule given, vertical sides will not change in length but horizontal sides will be doubled in length. Some angles will get larger [e.g. the angle determined by (1, 1), (0, 0), and (–1, 1)], some will get smaller [e.g., the an ...
... angle measures because the position of the original figure matters. For the rule given, vertical sides will not change in length but horizontal sides will be doubled in length. Some angles will get larger [e.g. the angle determined by (1, 1), (0, 0), and (–1, 1)], some will get smaller [e.g., the an ...
Paired states of fermions in two dimensions with breaking of parity
... fermion and high Tc superconductors. Some nonzero l paired states generally have vanishing energy gap at some points on the Fermi surface (for weak coupling), while others do not. While the absence of a transition is wellknown in the s-wave case, it seems to be less well known that in some of these ...
... fermion and high Tc superconductors. Some nonzero l paired states generally have vanishing energy gap at some points on the Fermi surface (for weak coupling), while others do not. While the absence of a transition is wellknown in the s-wave case, it seems to be less well known that in some of these ...
8th Grade Essential Learnings
... contrast with the constant rate of change of linear functions − Construct and compare linear, quadratic, and exponential models and solve problems (Common Core State Standards Initiative, ...
... contrast with the constant rate of change of linear functions − Construct and compare linear, quadratic, and exponential models and solve problems (Common Core State Standards Initiative, ...
Multiphoton population transfer in systems violating the classical twist condition: A... study of separatrix crossing in phase space
... atom using microwaves [5,6] and trains of impulsive kicks [7]. Furthermore, the same method has been theoretically ...
... atom using microwaves [5,6] and trains of impulsive kicks [7]. Furthermore, the same method has been theoretically ...
Scale invariance
In physics, mathematics, statistics, and economics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry.In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilatations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity.In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale.In quantum field theory, scale invariance has an interpretation in terms of particle physics. In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved.In statistical mechanics, scale invariance is a feature of phase transitions. The key observation is that near a phase transition or critical point, fluctuations occur at all length scales, and thus one should look for an explicitly scale-invariant theory to describe the phenomena. Such theories are scale-invariant statistical field theories, and are formally very similar to scale-invariant quantum field theories.Universality is the observation that widely different microscopic systems can display the same behaviour at a phase transition. Thus phase transitions in many different systems may be described by the same underlying scale-invariant theory.In general, dimensionless quantities are scale invariant. The analogous concept in statistics are standardized moments, which are scale invariant statistics of a variable, while the unstandardized moments are not.