H-Measures and Applications - International Mathematical Union
... Even if we do not know what atoms really are they do appear as tiny obstacles and we have then to face the difficulty of working with at least two scales, a microscopic one and a macroscopic one. In some way the practical goal of quantum physics is to compute corrections in the effective equations s ...
... Even if we do not know what atoms really are they do appear as tiny obstacles and we have then to face the difficulty of working with at least two scales, a microscopic one and a macroscopic one. In some way the practical goal of quantum physics is to compute corrections in the effective equations s ...
Phys. Rev. Lett. 103, 265302
... (c) h-dependence of c ¼ 2gc at fixed J, for the 1D bosonic (squares) and quantum Ising models (solid line). Here m ¼ 2 þ h and all other parameters as in Fig. 3. ...
... (c) h-dependence of c ¼ 2gc at fixed J, for the 1D bosonic (squares) and quantum Ising models (solid line). Here m ¼ 2 þ h and all other parameters as in Fig. 3. ...
Creation of long-term coherent optical memory via controlled nonlinear interactions
... that affect ψ2 (but not ψ1 ), and imaging of the dynamics is facilitated by the 2D structure of the condensate. An order of magnitude increase in the overall revival fidelity can be achieved by such transverse localization of the input light pulse or - depending on the application - by inversion of ...
... that affect ψ2 (but not ψ1 ), and imaging of the dynamics is facilitated by the 2D structure of the condensate. An order of magnitude increase in the overall revival fidelity can be achieved by such transverse localization of the input light pulse or - depending on the application - by inversion of ...
Document
... General idea: 8, 10, anti-10, etc are various excitations of the same mean field properties are interrelated Example [Gudagnini ‘84] ...
... General idea: 8, 10, anti-10, etc are various excitations of the same mean field properties are interrelated Example [Gudagnini ‘84] ...
Multiphoton antiresonance M. I. Dykman and M. V. Fistul
... We consider not too large amplitudes of the driving field A, so that the oscillator anharmonicity is small, and in particular 兩␥兩q2 Ⰶ 20 for typical q. We also assume that ␥ and ␦ have the same sign. If there is a cubic term ␣q3 / 3 in the potential energy, its major effect of interest for this pa ...
... We consider not too large amplitudes of the driving field A, so that the oscillator anharmonicity is small, and in particular 兩␥兩q2 Ⰶ 20 for typical q. We also assume that ␥ and ␦ have the same sign. If there is a cubic term ␣q3 / 3 in the potential energy, its major effect of interest for this pa ...
Linear Momentum and Collisions
... This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permit ...
... This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permit ...
- IISER
... ii. BIO 325 Advanced Biology Lab-II iii. BIO 412 Advanced Biology Lab-III 2. Elective courses a. ...
... ii. BIO 325 Advanced Biology Lab-II iii. BIO 412 Advanced Biology Lab-III 2. Elective courses a. ...
Paper
... using a Raman process without y-momentum transfer, or, equivalently, by inducing tunneling through lattice modulation [37–39]. In the case of two different magnetic moments, one could also perform dynamic experiments, where laser parameters are modified in such a way that one switches either suddenl ...
... using a Raman process without y-momentum transfer, or, equivalently, by inducing tunneling through lattice modulation [37–39]. In the case of two different magnetic moments, one could also perform dynamic experiments, where laser parameters are modified in such a way that one switches either suddenl ...
URL - StealthSkater
... Universe. We have trouble visualizing more than 3-dimensions. Einstein proved that time can not be separated from 3-dimensional space, although it is hard to picture what space-time looks like. In retrospect, had Einstein followed course and allowed for more dimensions as he did with time, he might ...
... Universe. We have trouble visualizing more than 3-dimensions. Einstein proved that time can not be separated from 3-dimensional space, although it is hard to picture what space-time looks like. In retrospect, had Einstein followed course and allowed for more dimensions as he did with time, he might ...
Slides
... choice of the form of the E-M tensor, because to add a surface term will not change the conservation law satisfied by the E-M tensor. • The symmetric one is prefered because it is gauge invariant and the Einstain gravitation equation needs symmetric one. • In fact the E-M tensor density of em-field ...
... choice of the form of the E-M tensor, because to add a surface term will not change the conservation law satisfied by the E-M tensor. • The symmetric one is prefered because it is gauge invariant and the Einstain gravitation equation needs symmetric one. • In fact the E-M tensor density of em-field ...
Review Problems for Test 1
... n=1 (−1) (n!(5·7···(2n+3))) ), y2 = x (1+2x+ n=2 (−1) (n!(1·3···(2n−3))) 3. Show that x = 0 is a regular singular point to the Laguerre equation xy 00 + (1 − x)y 0 + py = 0. Show that r = 0 is a double root for the indicial equation and compute the recurrence formula for a series solution to this di ...
... n=1 (−1) (n!(5·7···(2n+3))) ), y2 = x (1+2x+ n=2 (−1) (n!(1·3···(2n−3))) 3. Show that x = 0 is a regular singular point to the Laguerre equation xy 00 + (1 − x)y 0 + py = 0. Show that r = 0 is a double root for the indicial equation and compute the recurrence formula for a series solution to this di ...
Formulation of Liouville`s Theorem for Grand Ensemble Molecular
... We propose a problem that, in our knowledge and at least in the field of molecular simulation, has not been explicitly treated before, namely whether or not it is possible a rigorous formulation of Liouville’s theorem (and corresponding operator) when a system is characterized by a varying number of ...
... We propose a problem that, in our knowledge and at least in the field of molecular simulation, has not been explicitly treated before, namely whether or not it is possible a rigorous formulation of Liouville’s theorem (and corresponding operator) when a system is characterized by a varying number of ...
Simple, Complex, Super-complex Systems
... presented in rather different ways. The differences are often so remarkable that one may ask whether there is in fact anything like “the” theory of systems. Thirdly, it is worth mentioning that more often than not a number of conceptual confusions continue to pester the development of system theory. ...
... presented in rather different ways. The differences are often so remarkable that one may ask whether there is in fact anything like “the” theory of systems. Thirdly, it is worth mentioning that more often than not a number of conceptual confusions continue to pester the development of system theory. ...
A New Quantum Behaved Particle Swarm Optimization
... following Newtonian mechanics. However if we consider quantum mechanics, then the term trajectory is meaningless, because xi and vi of a particle cannot be determined simultaneously according to uncertainty principle. Therefore, if individual particles in a PSO system have quantum behavior, the perf ...
... following Newtonian mechanics. However if we consider quantum mechanics, then the term trajectory is meaningless, because xi and vi of a particle cannot be determined simultaneously according to uncertainty principle. Therefore, if individual particles in a PSO system have quantum behavior, the perf ...
Commutation relations for functions of operators
... where the 共 ⬘兲 symbol denotes differentiation with respect to the variable. The derivation of Eqs. 共6兲 and 共7兲 is a typical and almost obligatory exercise in a modern text on quantum mechanics. The standard way of proceeding is to consider the commutator of x with increasing powers of p, to use indu ...
... where the 共 ⬘兲 symbol denotes differentiation with respect to the variable. The derivation of Eqs. 共6兲 and 共7兲 is a typical and almost obligatory exercise in a modern text on quantum mechanics. The standard way of proceeding is to consider the commutator of x with increasing powers of p, to use indu ...
Quantum Mechanics: what is it and why is it interesting? Dr. Neil Shenvi
... 1788 – Lagrange’s Mecanique Analytique 1834 – Hamiltonian mechanics 1864 – Maxwell’s equations 1900 – Boltzmann’s entropy equation ...
... 1788 – Lagrange’s Mecanique Analytique 1834 – Hamiltonian mechanics 1864 – Maxwell’s equations 1900 – Boltzmann’s entropy equation ...
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.