Mathematical Aspects of Quantum Theory and Quantization Summer
... What topics will be discussed in these lectures? The general subject is quantum theory, as a physical theory, but with an emphasis on its mathematical structure. The mathematics for this is functional analysis, Hilbert space theory, and more particular the theory of linear operators. I explain what ...
... What topics will be discussed in these lectures? The general subject is quantum theory, as a physical theory, but with an emphasis on its mathematical structure. The mathematics for this is functional analysis, Hilbert space theory, and more particular the theory of linear operators. I explain what ...
hep-th/0302002 PDF - at www.arxiv.org.
... nonderivative, coupling between the fields. Some non-correct assertions in the literature are corrected. The calculations and derivations are relatively detailed; one of the reasons being that they or part of them are directly or, possibly, mutatis mutandis used in the next sections. Section 5 deals ...
... nonderivative, coupling between the fields. Some non-correct assertions in the literature are corrected. The calculations and derivations are relatively detailed; one of the reasons being that they or part of them are directly or, possibly, mutatis mutandis used in the next sections. Section 5 deals ...
2 Quantum Theory of Spin Waves
... The elementary excitations of coupled spin systems in solids are called spin waves. In this chapter, we will introduce the quantum theory of these excitations at low temperatures. The two primary interaction mechanisms for spins are magnetic dipole–dipole coupling and a mechanism of quantum mechanic ...
... The elementary excitations of coupled spin systems in solids are called spin waves. In this chapter, we will introduce the quantum theory of these excitations at low temperatures. The two primary interaction mechanisms for spins are magnetic dipole–dipole coupling and a mechanism of quantum mechanic ...
Calculating Floquet states of large quantum systems: A
... An alternative option is to expand the time-dependent Hamiltonian into a Fourier series and, and then truncating it, by keeping 2F + 1 harmonics kω, k = −F, ..., 0, ..., F only, to reduce the problem to the diagonalization of a time-independent superHamiltonian [8, 21]. This is a reliable method to ...
... An alternative option is to expand the time-dependent Hamiltonian into a Fourier series and, and then truncating it, by keeping 2F + 1 harmonics kω, k = −F, ..., 0, ..., F only, to reduce the problem to the diagonalization of a time-independent superHamiltonian [8, 21]. This is a reliable method to ...
Dirac Operators on Noncommutative Spacetimes ?
... equivalent. It is thus not clear which operator we should choose, and that state of affairs certainly is not satisfactory. To improve on it, we will propose an abstract characterization of a Dirac operator on noncommutative curved spacetimes, in terms of a minimal set of axioms. Namely, it should be ...
... equivalent. It is thus not clear which operator we should choose, and that state of affairs certainly is not satisfactory. To improve on it, we will propose an abstract characterization of a Dirac operator on noncommutative curved spacetimes, in terms of a minimal set of axioms. Namely, it should be ...
Kitaev - Anyons
... A different kind of state is observed at the filling factor m = 5/2, though it is more fragile and less studied experimentally. There is much evidence suggesting that this system is described by a beautiful theory proposed by Moore and Read [14,15]. The Moore–Read state admits non-Abelian anyons with ...
... A different kind of state is observed at the filling factor m = 5/2, though it is more fragile and less studied experimentally. There is much evidence suggesting that this system is described by a beautiful theory proposed by Moore and Read [14,15]. The Moore–Read state admits non-Abelian anyons with ...
Gauge and Matter Fields on a Lattice - Generalizing
... operator Z(γl ), then the charge at vertex v1 is annihilated by the action of Zv1 leaving a single charge at v2 . . . . . . . . . . . . . . . . . . . . . . . . . Two plaquette excitations (fluxes) are created at plaquettes p1 and p2 by the action of a σ x operator at the link in between, at the same ...
... operator Z(γl ), then the charge at vertex v1 is annihilated by the action of Zv1 leaving a single charge at v2 . . . . . . . . . . . . . . . . . . . . . . . . . Two plaquette excitations (fluxes) are created at plaquettes p1 and p2 by the action of a σ x operator at the link in between, at the same ...
A Matrix Realignment Method for Recognizing Entanglement
... systems, which is based on a realigned matrix constructed from the density matrix. It shows dramatic ability to identify many of the bounded entangled states discussed in the literature. Based on this criterion and the Peres-Horodecki criterion [i.e., PPT (positive partial transposition) criterion], ...
... systems, which is based on a realigned matrix constructed from the density matrix. It shows dramatic ability to identify many of the bounded entangled states discussed in the literature. Based on this criterion and the Peres-Horodecki criterion [i.e., PPT (positive partial transposition) criterion], ...
Commun. Math. Phys. 110, 33-49
... control of the dynamics for finite times, and so is amenable to rigorous analysis. The analysis of the conductance is harder because it involves long times: The conductance is defined as the asymptotic (in time) ratio of current to emf, assuming a constant emf for large times. This limit introduces ...
... control of the dynamics for finite times, and so is amenable to rigorous analysis. The analysis of the conductance is harder because it involves long times: The conductance is defined as the asymptotic (in time) ratio of current to emf, assuming a constant emf for large times. This limit introduces ...
Quantum Field Theory I
... The factor corresponding to an external leg is, as a rule, the product of two factors. Let us start with the simpler one. For the scalar field ϕ (representing a particle with zero spin) this factor is the simplest possible, it equals to 1. For other fields (representing particles with higher spins) ...
... The factor corresponding to an external leg is, as a rule, the product of two factors. Let us start with the simpler one. For the scalar field ϕ (representing a particle with zero spin) this factor is the simplest possible, it equals to 1. For other fields (representing particles with higher spins) ...
Quantum Symmetric States - UCLA Department of Mathematics
... The tail σ-algebra is the intersection of the σ-algebras generated by {xN , xN +1 , . . .} as N goes to ∞. Thus, the expectation E can be seen as an integral (w.r.t. a probability measure on the tail algebra) — that is, as a sort of convex combination — of expectations with respect to which the rand ...
... The tail σ-algebra is the intersection of the σ-algebras generated by {xN , xN +1 , . . .} as N goes to ∞. Thus, the expectation E can be seen as an integral (w.r.t. a probability measure on the tail algebra) — that is, as a sort of convex combination — of expectations with respect to which the rand ...
Research Statement Introduction Gabor Lippner
... hence is not 2 edge-colorable. This construction has later been generalized to 2d regular graphs, but both the existence of a perfect matching and the existence of edge-coloring is unresolved for odd degrees. On the positive side, motivated by questions about random processes on groups, Lyons and Na ...
... hence is not 2 edge-colorable. This construction has later been generalized to 2d regular graphs, but both the existence of a perfect matching and the existence of edge-coloring is unresolved for odd degrees. On the positive side, motivated by questions about random processes on groups, Lyons and Na ...
quantum states satisfying classical probability constraints
... a separable representation of ρsep . Then, for example, T122 = m ξm ρ1 ⊗ ρ2 ⊗ ρ2 is a density source-operator for ρsep . Hence, any separable state is a DSO state. However, the converse is not true and a DSO state may be nonseparable. In section 2.1.1, we consider examples of nonseparable DSO states ...
... a separable representation of ρsep . Then, for example, T122 = m ξm ρ1 ⊗ ρ2 ⊗ ρ2 is a density source-operator for ρsep . Hence, any separable state is a DSO state. However, the converse is not true and a DSO state may be nonseparable. In section 2.1.1, we consider examples of nonseparable DSO states ...
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... angle rotations can be built up as products of large numbers of small angle rotations to extend this relation to arbitrary angles. When defining the angular momentum in quantum mechanics, we have some of the same issues we faced earlier when trying to define linear momentum in quantum mechanics by t ...
... angle rotations can be built up as products of large numbers of small angle rotations to extend this relation to arbitrary angles. When defining the angular momentum in quantum mechanics, we have some of the same issues we faced earlier when trying to define linear momentum in quantum mechanics by t ...
The Effective Action for Local Composite Operators Φ2(x) and Φ4(x)
... cently, an expansion of the effective action for the operator Φ2 (x) in terms of two-particle-point-irreducible (2PPI) diagrams was given [8, 9]. The result is implicit but enables us to calculate the effective potential [9] and the twoparticle composite propagator [10]. The Gaussian effective acti ...
... cently, an expansion of the effective action for the operator Φ2 (x) in terms of two-particle-point-irreducible (2PPI) diagrams was given [8, 9]. The result is implicit but enables us to calculate the effective potential [9] and the twoparticle composite propagator [10]. The Gaussian effective acti ...