POISSON BOUNDARIES OVER LOCALLY COMPACT
... L∞ (G) by certain quantum groups, such as its dual (quantum) group von Neumann algebra V N (G) or quantum groups arising from mathematical physics; in another direction, one can perform the quantum mechanical passage from L∞ (G) to B(L2 (G)). Poisson boundaries over discrete quantum groups were firs ...
... L∞ (G) by certain quantum groups, such as its dual (quantum) group von Neumann algebra V N (G) or quantum groups arising from mathematical physics; in another direction, one can perform the quantum mechanical passage from L∞ (G) to B(L2 (G)). Poisson boundaries over discrete quantum groups were firs ...
Workshop on Spectral Geometry General Information
... estimates for the magnetic Laplacian on discrete graphs with signatures and on closed Riemannian manifolds with magnetic potentials. These results relate eigenvalues, magnetic fields, Ricci curvature and Cheeger type constants. This is based on joint work with Michela Egidi, Florentin M\"unch, and N ...
... estimates for the magnetic Laplacian on discrete graphs with signatures and on closed Riemannian manifolds with magnetic potentials. These results relate eigenvalues, magnetic fields, Ricci curvature and Cheeger type constants. This is based on joint work with Michela Egidi, Florentin M\"unch, and N ...
Localization and the Integer Quantum Hall effect
... We now go back to the ideas of the [first] section, but holding on to the notion that backscattering is the cause of resistance. It turns out (as shall be justified in the following section) that for localization in a large magnetic field, there is an extended state but only at one energy Ec in the ...
... We now go back to the ideas of the [first] section, but holding on to the notion that backscattering is the cause of resistance. It turns out (as shall be justified in the following section) that for localization in a large magnetic field, there is an extended state but only at one energy Ec in the ...
Chapter 4 Quantum Entanglement
... What are the implications? To some people, the peculiar correlations unmasked by Bell’s theorem call out for a deeper explanation than quantum mechanics seems to provide. They see the EPR phenomenon as a harbinger of new physics awaiting discovery. But they may be wrong. We have been waiting over 60 ...
... What are the implications? To some people, the peculiar correlations unmasked by Bell’s theorem call out for a deeper explanation than quantum mechanics seems to provide. They see the EPR phenomenon as a harbinger of new physics awaiting discovery. But they may be wrong. We have been waiting over 60 ...
Quantum Magnetism
... aways a much larger effect, and the dipolar interactions are therefore normally neglected in the discussions of magnetic interactions in solids. Exchange arises because, e.g., two quantum mechanical spins 1/2 (in isolation) can be in either a spin triplet (total S = 1), or singlet (total S = 0). The ...
... aways a much larger effect, and the dipolar interactions are therefore normally neglected in the discussions of magnetic interactions in solids. Exchange arises because, e.g., two quantum mechanical spins 1/2 (in isolation) can be in either a spin triplet (total S = 1), or singlet (total S = 0). The ...
here
... variable that is constant along trajectories is called a constant of motion. Its value may differ from trajectory to trajectory. The hamiltonian H = T + V is a conserved quantity for conservative systems (i.e. where the force is the negative gradient of a scalar potential). ẋ = ...
... variable that is constant along trajectories is called a constant of motion. Its value may differ from trajectory to trajectory. The hamiltonian H = T + V is a conserved quantity for conservative systems (i.e. where the force is the negative gradient of a scalar potential). ẋ = ...
Elementary Introduction to Quantum Field Theory in Curved Spacetime
... where η µν = diag(1, −1, −1, −1) is the Minkowski metric (in this chapter we consider only the flat spacetime) and the Greek indices label four-dimensional coordinates: x0 ≡ t and (x1 , x2 , x3 ) ≡ x. Using Eq. (10), one can also express the action (11) directly through the (complex-valued) modes φk ...
... where η µν = diag(1, −1, −1, −1) is the Minkowski metric (in this chapter we consider only the flat spacetime) and the Greek indices label four-dimensional coordinates: x0 ≡ t and (x1 , x2 , x3 ) ≡ x. Using Eq. (10), one can also express the action (11) directly through the (complex-valued) modes φk ...
Macroscopic Distinguishability Between Quantum States
... the thermodynamical limit, when the number of degrees of freedom of the system becomes large (in the limit of a large number of microscopic sub-systems). Yet, there is no special objection why quantum mechanics should not be generally applicable, even to macroscopic systems. Indeed, macroscopic phen ...
... the thermodynamical limit, when the number of degrees of freedom of the system becomes large (in the limit of a large number of microscopic sub-systems). Yet, there is no special objection why quantum mechanics should not be generally applicable, even to macroscopic systems. Indeed, macroscopic phen ...
Fun items for the teaching of mechanics
... 3. A sailboat is sailing downstream. The wind is blowing in the same direction of the stream. The velocity of the water is 3 m s-1 and the velocity of the wind is 5 m s-1. What is the maximum velocity that can be attained by the sailboat? 4. Two jets X and Y flew from A to B a distance of 4000 km. J ...
... 3. A sailboat is sailing downstream. The wind is blowing in the same direction of the stream. The velocity of the water is 3 m s-1 and the velocity of the wind is 5 m s-1. What is the maximum velocity that can be attained by the sailboat? 4. Two jets X and Y flew from A to B a distance of 4000 km. J ...
Atomic Spectroscopy
... higher values of angular momentum (d, f ) are identical to the hydrogen energy spectrum. The spectrum of Na is shown in Fig. 2. One can immediately see that there are many more optical transitions because of the lifted degeneracy of energy states with different angular momenta. However, not all elec ...
... higher values of angular momentum (d, f ) are identical to the hydrogen energy spectrum. The spectrum of Na is shown in Fig. 2. One can immediately see that there are many more optical transitions because of the lifted degeneracy of energy states with different angular momenta. However, not all elec ...
Inequivalence of pure state ensembles for open quantum systems
... Also, let us consider only stationary ensembles for ρ̂ss . Clearly, once the system has reached steady-state then such a stationary ensemble will represent the system for all times t. Now, if the ignorance interpretation were to hold for such an ensemble then it should be possible, in principle, for ...
... Also, let us consider only stationary ensembles for ρ̂ss . Clearly, once the system has reached steady-state then such a stationary ensemble will represent the system for all times t. Now, if the ignorance interpretation were to hold for such an ensemble then it should be possible, in principle, for ...
referring
... Sec. III B兴 by essentially guessing the appropriate generalization of their classical counterparts. We are unaware of any evidence that can settle the issue. In any case, our analysis shows that it is possible to read Heisenberg’s paper as providing a complete 共if limited兲 calculational method, the ...
... Sec. III B兴 by essentially guessing the appropriate generalization of their classical counterparts. We are unaware of any evidence that can settle the issue. In any case, our analysis shows that it is possible to read Heisenberg’s paper as providing a complete 共if limited兲 calculational method, the ...
