Quantized quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity Deng-Shan Wang, Xing-Hua Hu,
... |x|,|y| → ∞ we have ψn → 0 for solutions ψn in Eqs. (2) and (3) with Eq. (4), thus they are localized bound state solutions. In the above construction, it is observed that the number of zero points of function η in Eq. (4) is equal to that of function Kummer U[−µ/(2ω), 1/2, ω (x − y)2 /2], which str ...
... |x|,|y| → ∞ we have ψn → 0 for solutions ψn in Eqs. (2) and (3) with Eq. (4), thus they are localized bound state solutions. In the above construction, it is observed that the number of zero points of function η in Eq. (4) is equal to that of function Kummer U[−µ/(2ω), 1/2, ω (x − y)2 /2], which str ...
Quantum transfer operators and chaotic scattering Stéphane
... argument that one quantum state occupies a volume ∼ hd in phase space). Such operators have been called “open quantum maps”. Let us now assume that the map T has chaotic properties: the nonwandering set Γ is a fractal set included inside B(0, R), and T is uniformly hyperbolic on Γ. We may then expec ...
... argument that one quantum state occupies a volume ∼ hd in phase space). Such operators have been called “open quantum maps”. Let us now assume that the map T has chaotic properties: the nonwandering set Γ is a fractal set included inside B(0, R), and T is uniformly hyperbolic on Γ. We may then expec ...
An Introduction to the Standard Model and the Electroweak Force
... This Thesis is brought to you for free and open access by the Carl Goodson Honors Program at Scholarly Commons @ Ouachita. It has been accepted for inclusion in Honors Theses by an authorized administrator of Scholarly Commons @ Ouachita. For more information, please contact ...
... This Thesis is brought to you for free and open access by the Carl Goodson Honors Program at Scholarly Commons @ Ouachita. It has been accepted for inclusion in Honors Theses by an authorized administrator of Scholarly Commons @ Ouachita. For more information, please contact ...
Part I
... using results for the Mean Square Deviation: (ΔE)2 = E2 - (Ē)2 = 2lnZ/2 = - Ē/ CV can be re-written as: ...
... using results for the Mean Square Deviation: (ΔE)2 = E2 - (Ē)2 = 2lnZ/2 = - Ē/ CV can be re-written as: ...
Chapter 1 Introduction: Why are quantum many
... exhaustively. Only a statistical description (based on bulk properties) can be input as initial conditions into a model and because of this, only bulk statistical properties of the model will correspond accurately to the behavior of the physical system under study. In quantum systems, we have (in a ...
... exhaustively. Only a statistical description (based on bulk properties) can be input as initial conditions into a model and because of this, only bulk statistical properties of the model will correspond accurately to the behavior of the physical system under study. In quantum systems, we have (in a ...
PowerPoint format
... Medical science: determine geometric ways in which pathological and normal classes differ Diagnostic: determine if particular patient’s geometry is in pathological or normal class Educational: communicate anatomic variability in atlases Priors for segmentation Monte Carlo generation of images ...
... Medical science: determine geometric ways in which pathological and normal classes differ Diagnostic: determine if particular patient’s geometry is in pathological or normal class Educational: communicate anatomic variability in atlases Priors for segmentation Monte Carlo generation of images ...
PHYS2042 Quantum Mechanics (Part II)
... We would now like to use this equation to study the structure of atoms in a fully quantum manner. In particular, we will consider the hydrogen atom since it is the most simple atom consisting of a single electron. You have already studied Bohr’s model of the hydrogen atom. Despite it’s spectacular s ...
... We would now like to use this equation to study the structure of atoms in a fully quantum manner. In particular, we will consider the hydrogen atom since it is the most simple atom consisting of a single electron. You have already studied Bohr’s model of the hydrogen atom. Despite it’s spectacular s ...
Physics Subject Knowledge Enhancement course
... • The courses are suitable for new graduates and those who are looking for a career change, with experience of the subject to at least A-level standard. • This could be through holding an A/AS-level in the subject, having an element of it in your degree course and/or occupational experience of the s ...
... • The courses are suitable for new graduates and those who are looking for a career change, with experience of the subject to at least A-level standard. • This could be through holding an A/AS-level in the subject, having an element of it in your degree course and/or occupational experience of the s ...
The Dimensions of M
... An additional problem is that the string states only include bosonic particles. However, it is known that nature certainly contains fermions, such as electrons and quarks. Since supersymmetry is the invariance of a theory under the interchange of bosons and fermions, it may come as no surprise, post ...
... An additional problem is that the string states only include bosonic particles. However, it is known that nature certainly contains fermions, such as electrons and quarks. Since supersymmetry is the invariance of a theory under the interchange of bosons and fermions, it may come as no surprise, post ...
Function Guided Notes
... If, for each value of x in the domain, the pencil passes through only one point of the graph, then the graph represents a function. ...
... If, for each value of x in the domain, the pencil passes through only one point of the graph, then the graph represents a function. ...
M. Sc. Courses in Physics (Session 2016
... statistical definition of thermodynamic quantities, computation of partition functions of some standard systems. Unit-II: Statistical Properties System of linear harmonic oscillators in the canonical ensemble; grand canonical ensemble and its partition function; chemical potential; Partition functio ...
... statistical definition of thermodynamic quantities, computation of partition functions of some standard systems. Unit-II: Statistical Properties System of linear harmonic oscillators in the canonical ensemble; grand canonical ensemble and its partition function; chemical potential; Partition functio ...
quantum-gravity-presentation
... Quantum Gravity: Why so Difficult? • Don’t Buy the Tickets Quite Yet (III) • What Does it Mean to Have an Infinite Series with Terms of Increasing Dimension? • If You “Cutoff” the Series, You Can Apparently Fiddle with the Resulting Equations to Get Something With a Physical Meaning • But You Canno ...
... Quantum Gravity: Why so Difficult? • Don’t Buy the Tickets Quite Yet (III) • What Does it Mean to Have an Infinite Series with Terms of Increasing Dimension? • If You “Cutoff” the Series, You Can Apparently Fiddle with the Resulting Equations to Get Something With a Physical Meaning • But You Canno ...
Renormalization group
In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle (cf. Compton wavelength).A change in scale is called a ""scale transformation"". The renormalization group is intimately related to ""scale invariance"" and ""conformal invariance"", symmetries in which a system appears the same at all scales (so-called self-similarity). (However, note that scale transformations are included in conformal transformations, in general: the latter including additional symmetry generators associated with special conformal transformations.)As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller scale, with different parameters describing the components of the system. The components, or fundamental variables, may relate to atoms, elementary particles, atomic spins, etc. The parameters of the theory typically describe the interactions of the components. These may be variable ""couplings"" which measure the strength of various forces, or mass parameters themselves. The components themselves may appear to be composed of more of the self-same components as one goes to shorter distances.For example, in quantum electrodynamics (QED), an electron appears to be composed of electrons, positrons (anti-electrons) and photons, as one views it at higher resolution, at very short distances. The electron at such short distances has a slightly different electric charge than does the ""dressed electron"" seen at large distances, and this change, or ""running,"" in the value of the electric charge is determined by the renormalization group equation.