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Kinetics of decay of metastable gas phase of polarized atomic
Kinetics of decay of metastable gas phase of polarized atomic

... by the small parameter (1.2). In this paper we develop a quantum-mechanical theory of this depolarization process (see Sec. 2). The presence of an exchange depolarization mechanism in pair collisions was actually first pointed out by Brown. To determine the probability of the depolarization, he modi ...
arXiv:math/0606118v4 [math.PR] 5 Dec 2006
arXiv:math/0606118v4 [math.PR] 5 Dec 2006

... control was explored in discrete time using the operational formalism of Davies [27], which is the precursor of quantum filtering theory. Belavkin developed further the theory of quantum filtering in a series of articles [8, 10, 12], and in [10] the use of dynamic programming for feedback control in ...
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BUSSTEPP Lectures on String Theory

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... [15, 51, 107]. Excluding scaling, ultracold atomic systems behave the same with their only differences being characterized by a few parameters such as the scattering length. At a more fundamental level, such universal behaviors have their origin in the universal ultracold two-body interaction as des ...
Problem 7.54 A Ball Hits a Wall Elastically
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... the ball and the wall is Δt, and this collision is completely elastic. Friction is negligible, so the ball does not start spinning. In this idealized collision, the force exerted on the ball by the wall is parallel to the x axis. ...
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Quantum scattering

... In this way, for any finite value of the radius R of the box, we have mapped our scattering system into a bound system with a spectral density d(E; R) over discrete eigenenergies En (R). It is therefore important that our scattering potential was chosen to be short-ranged to start with. (Which expla ...
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... the microscopic information is not important and short distances degrees of freedom can be integrated out. Then, according to the Wilsonian renormalization group flow, the resulting theory will be described only by a finite number of relevant and marginal terms [4]. The idea of integrating out micro ...
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Driven Bose-Hubbard model with a parametrically modulated

... of externally driven systems are parametric oscillators in which the characteristic frequency is periodically modulated. Already the classical Kapitza pendulum is known for its peculiar dynamics [20] which is stabilized by properly choosing the driving parameters. The parametric quantum harmonic osc ...
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Symmetries and Conservation Laws

... physics. On the practical side, one can use conservation of energy, momentum, etc. to unravel many aspects of the motion of a system without having to explicitly integrate the equations of motion. Indeed for systems with one degree of freedoms, a conservation law usually determines everything! More ...
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Macroscopic superposition states and decoherence by quantum

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Inferring latent structures via information inequalities

... Two points are made in Sec. 4.2, treating an example where the direction of causation between a set of variables is to be inferred. Firstly, that marginal entropies of few variables can carry non-trivial information about conditional independencies encoded in a larger number of variables. This may h ...
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PHYSICS 430 Lecture Notes on Quantum Mechanics

... perhaps a few seconds, the baseball will return to your hand. Denote the height of the baseball, as a function of time, as x(t); this is the trajectory of the baseball. If we make a plot of x as a function of t, then any trajectory has the form of a parabola (in a uniform gravitational field, neglec ...
electric fields and potentials from continuous charge distributions
electric fields and potentials from continuous charge distributions

... evaluate this integral. Since this is a physics course, your attention will focus on step a. Step b can range in difficulty from trivial to impossible dependinq upon the complexity of the charge distribution and upon your facility at evaluatin~ integrals. Although we shall not emphasize the mathemat ...
What quantum computers may tell us about quantum mechanics
What quantum computers may tell us about quantum mechanics

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Quantum groups and integrable lattice models UMN Math Physics Seminar

... This operator (”R-matrix “) captures contributions of a single vertex to the partition function. Consider an (N + 1)-fold tensor product V0 ⊗ V1 ⊗ · · · ⊗ VN (Vi = V ) and let Rij be the operator acting on the Vi ⊗ Vj component of this product as R and as identity on any other Vl . ...
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full text

... Monodromy prevents defining the global second quantum number for the entire lattice of quantum states of the spherical pendulum system. Using the elementary cell continuation method in Sec. I C. we can of course define smooth sequences of states, but we will fail when we try to extend them to the wh ...
Efficient quantum algorithms for some instances of the non
Efficient quantum algorithms for some instances of the non

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Photodissociation Dynamics of Molecular Fluorine in an Argon

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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.
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