Symplectic Geometry and Geometric Quantization
... formalize the notion of a classical mechanical system. Then we will show how they define and perform its quantization in this framework. The question of quantization consists in assigning a quantum system to a classical one. This problem is still very timely, since there is in general no unique way ...
... formalize the notion of a classical mechanical system. Then we will show how they define and perform its quantization in this framework. The question of quantization consists in assigning a quantum system to a classical one. This problem is still very timely, since there is in general no unique way ...
The path integral representation kernel of evolution operator in
... with the formula from [6, 7] shows that the latter does not contain the second summand in S0 , as well as there is a change in the corresponding numerical coefficient in the third summand r̃. Recall that in [6, 7] there is used a Feynman path integral defined in the configurational phase space, in c ...
... with the formula from [6, 7] shows that the latter does not contain the second summand in S0 , as well as there is a change in the corresponding numerical coefficient in the third summand r̃. Recall that in [6, 7] there is used a Feynman path integral defined in the configurational phase space, in c ...
A Quantum Version of The Spectral Decomposition Theorem of
... Markov operators satisfy important properties that will be crucial in the derivation of a quantum version of Spectral Decomposition Theorem (see [1], pag. 33). Theorem 1. Let (X, Σ, µ) be a σ-algebra and let f ∈ L1 . If P is a Markov operator then: (I) kP f k ≤ kf k ( contractive property) (II) |P f ...
... Markov operators satisfy important properties that will be crucial in the derivation of a quantum version of Spectral Decomposition Theorem (see [1], pag. 33). Theorem 1. Let (X, Σ, µ) be a σ-algebra and let f ∈ L1 . If P is a Markov operator then: (I) kP f k ≤ kf k ( contractive property) (II) |P f ...
Solid State Physics from the Mathematicians` Point of View
... space R3 , and hence would not be interpretable in terms of any probability. On the other hand, Bloch and others defined a particular type of lattice and formulated the equations for the eigenfunctions on them. We could take that lattice and factor ”the space” by it, working on the factor space for ...
... space R3 , and hence would not be interpretable in terms of any probability. On the other hand, Bloch and others defined a particular type of lattice and formulated the equations for the eigenfunctions on them. We could take that lattice and factor ”the space” by it, working on the factor space for ...
ψ ε
... comparing the dynamics associated to (1.9) to the free dynamics ei 2 ∆ . In the above fort mula, we have incorporated the information that ei 2 ∆ is unitary on H 1 (Rd ), but not on Σ (see e.g. [13]). We can now state the nonlinear analogue to Theorem 1.3. Since Theorem 1.4 requires d > 3, we natura ...
... comparing the dynamics associated to (1.9) to the free dynamics ei 2 ∆ . In the above fort mula, we have incorporated the information that ei 2 ∆ is unitary on H 1 (Rd ), but not on Σ (see e.g. [13]). We can now state the nonlinear analogue to Theorem 1.3. Since Theorem 1.4 requires d > 3, we natura ...
Probability Current and Current Operators in Quantum Mechanics 1
... momentum current is zero. The second term is caused by the vector potential, and just depends on the square of the wave function at the point of interest. In fact, it really depends on the electric charge density, ρe = e|ψ|2 . This is a curious term. The vector potential needed to describe some EM f ...
... momentum current is zero. The second term is caused by the vector potential, and just depends on the square of the wave function at the point of interest. In fact, it really depends on the electric charge density, ρe = e|ψ|2 . This is a curious term. The vector potential needed to describe some EM f ...
Non-Hermitian Hamiltonians of Lie algebraic type
... • Calculated conditions and appropriate metrics with respect to which a large class of non Hermitian Hamiltonians bilinear in su(1,1) generators can be considered Hermitian. • The same non Hermitian Hamiltonians could be diagonalized and it was shown, whithout metrics, that although being non Hermit ...
... • Calculated conditions and appropriate metrics with respect to which a large class of non Hermitian Hamiltonians bilinear in su(1,1) generators can be considered Hermitian. • The same non Hermitian Hamiltonians could be diagonalized and it was shown, whithout metrics, that although being non Hermit ...
Toward an Understanding of Parochial Observables
... will call the problem of parochial observables. Ruetsche argues that there are certain observables, such as particle number, temperature, and net magnetization, that the Hilbert Space Conservative acquires and employs in physically significant explanations, and which the Imperialist and Universalist ...
... will call the problem of parochial observables. Ruetsche argues that there are certain observables, such as particle number, temperature, and net magnetization, that the Hilbert Space Conservative acquires and employs in physically significant explanations, and which the Imperialist and Universalist ...
quantum computing for computer scientists
... Boolean algebra conventions with the standard logical operators NOT, AND, OR, etc). A classical bit can only have two possible complementary states and most importantly, these states are required to be mutually exclusive. For example, if states a = True and NOT a = False, then bit a cannot simultane ...
... Boolean algebra conventions with the standard logical operators NOT, AND, OR, etc). A classical bit can only have two possible complementary states and most importantly, these states are required to be mutually exclusive. For example, if states a = True and NOT a = False, then bit a cannot simultane ...
Full text in PDF form
... κ by the relation κ ∼ T ∼ (GM )−1 , where M is the mass of the black hole [2]. Such a result has been obtained also for Rindler space-time [3, 4, 5, 6, 7], corresponding to an accelerating observer, with the difference that the surface gravity is replaced by the acceleration a of the observers (κ → ...
... κ by the relation κ ∼ T ∼ (GM )−1 , where M is the mass of the black hole [2]. Such a result has been obtained also for Rindler space-time [3, 4, 5, 6, 7], corresponding to an accelerating observer, with the difference that the surface gravity is replaced by the acceleration a of the observers (κ → ...
Lecture 4 Postulates of Quantum Mechanics, Operators
... Postulates of Quantum Mechanics Postulate 1 •The “Wave Function”, Ψ( x, y ,z ,t ), fully characterizes a quantum mechanical particle including it’s position, movement and temporal properties. • Ψ( x, y ,z ,t ) replaces the dynamical variables used in classical mechanics and fully describes a quantu ...
... Postulates of Quantum Mechanics Postulate 1 •The “Wave Function”, Ψ( x, y ,z ,t ), fully characterizes a quantum mechanical particle including it’s position, movement and temporal properties. • Ψ( x, y ,z ,t ) replaces the dynamical variables used in classical mechanics and fully describes a quantu ...
Quantum Probability Quantum Information Theory Quantum
... With these photon pairs, the very same experiment can be performed, but this time the polarizers are far apart, each one acting on its own photon. The same correlations are measured, say first between Pα on the left and Pβ on the right, then between Pα on the left and Pγ on the right, and finally be ...
... With these photon pairs, the very same experiment can be performed, but this time the polarizers are far apart, each one acting on its own photon. The same correlations are measured, say first between Pα on the left and Pβ on the right, then between Pα on the left and Pγ on the right, and finally be ...
Is spacetime a quantum error-correcting code?
... Illustrate how quantum error correction resolves the causal wedge puzzle, and how the operators deep in the entanglement wedge can be reconstructed. Realize exactly the Ryu-Takayanagi relation between boundary entanglement and bulk geometry (with small corrections in some cases). Allow flexibility i ...
... Illustrate how quantum error correction resolves the causal wedge puzzle, and how the operators deep in the entanglement wedge can be reconstructed. Realize exactly the Ryu-Takayanagi relation between boundary entanglement and bulk geometry (with small corrections in some cases). Allow flexibility i ...
Path Integrals in Quantum Mechanics
... where C is a ’correction’ operator according to the Baker-Campbell-Hausdorff formula. The correction operator is a series in with its lowest order term being C = 2 [T, V ] + O(3 ). We thus think of dividing the time interval [0, t] into N − 1 equidistant segments of length , where is assumed ...
... where C is a ’correction’ operator according to the Baker-Campbell-Hausdorff formula. The correction operator is a series in with its lowest order term being C = 2 [T, V ] + O(3 ). We thus think of dividing the time interval [0, t] into N − 1 equidistant segments of length , where is assumed ...
Kitaev - Anyons
... assumed that braiding is characterized just by phase factors, i.e., that the representation is one-dimensional. The corresponding anyons are called Abelian. But one can also consider multidimensional representations of the braid group; in this case the anyons are called non-Abelian. Actually, it may ...
... assumed that braiding is characterized just by phase factors, i.e., that the representation is one-dimensional. The corresponding anyons are called Abelian. But one can also consider multidimensional representations of the braid group; in this case the anyons are called non-Abelian. Actually, it may ...
Interacting Fock spaces: central limit theorems and quantum
... ii) we are able to construct the approximating sequence of random variables. The main technical tool used to reach such a theorem is given by a special class of interacting Fock spaces (IFS), namely the 1-mode type Free interacting Fock spaces. More precisely, after introducing a new basic operator ...
... ii) we are able to construct the approximating sequence of random variables. The main technical tool used to reach such a theorem is given by a special class of interacting Fock spaces (IFS), namely the 1-mode type Free interacting Fock spaces. More precisely, after introducing a new basic operator ...
Causality in quantum mechanics
... nature. We remember the past but not the future and we feel we have some control over future events but not over past events. The latter phenomenon is usually referred to as the principle of causality. Some authors [5] enunciate two causality principles: the strong and the weak. The strong principle ...
... nature. We remember the past but not the future and we feel we have some control over future events but not over past events. The latter phenomenon is usually referred to as the principle of causality. Some authors [5] enunciate two causality principles: the strong and the weak. The strong principle ...