Wigner`s Dynamical Transition State Theory in
... WBW05c] the fundamental framework for phase space TST is developed. The starting point is classical mechanics and a Hamiltonian function describing the system (the same as [Wig38]). The Hamiltonian can be expressed in any convenient set of coordinates, have any number, d, degrees of freedom (DoF) an ...
... WBW05c] the fundamental framework for phase space TST is developed. The starting point is classical mechanics and a Hamiltonian function describing the system (the same as [Wig38]). The Hamiltonian can be expressed in any convenient set of coordinates, have any number, d, degrees of freedom (DoF) an ...
Ph410 Physics of Quantum Computation1
... 3. States, Bits and Unitary Operations States and Bits. States of a system, or subsystem, involved in a computation will be denoted in various equivalent ways. A Greek symbol such as ψ will sometimes be used. When considering a quantum system, we will often embed the symbol in a ket, following Dirac ...
... 3. States, Bits and Unitary Operations States and Bits. States of a system, or subsystem, involved in a computation will be denoted in various equivalent ways. A Greek symbol such as ψ will sometimes be used. When considering a quantum system, we will often embed the symbol in a ket, following Dirac ...
The Automorphic Universe
... - µ1 and µ2 are equivalent (µ1 ∼ µ2 ) if µ1 << µ2 and µ2 << µ1 , that is if they have the same sets of zero measure - µ1 and µ2 are singular (µ1 ⊥µ2 ) if ∃ B ∈ B such that µ1 (B) = 0 and µ2 (B) = 1 If µ1 << µ2 , then Rthe Radon-Nikodym theorem says that there exist f ∈ L1 (X, B, µ2 ) ...
... - µ1 and µ2 are equivalent (µ1 ∼ µ2 ) if µ1 << µ2 and µ2 << µ1 , that is if they have the same sets of zero measure - µ1 and µ2 are singular (µ1 ⊥µ2 ) if ∃ B ∈ B such that µ1 (B) = 0 and µ2 (B) = 1 If µ1 << µ2 , then Rthe Radon-Nikodym theorem says that there exist f ∈ L1 (X, B, µ2 ) ...
Shannon Information Entropy in Position Space for Two
... and to characterize the probability distribution of samples. The Shannon entropy is defined by the one-electron charge density. Besides being a stronger version of the Heisenberg uncertainty principle of quantum mechanics [7], the Shannon entropy provides a measure of information about the probabili ...
... and to characterize the probability distribution of samples. The Shannon entropy is defined by the one-electron charge density. Besides being a stronger version of the Heisenberg uncertainty principle of quantum mechanics [7], the Shannon entropy provides a measure of information about the probabili ...
Measurability of Wilson loop operators
... Our protocol for superluminal signaling is based on the observation that Wilson loop measurement causes Cheshire charge to be transferred from Alice’s flux tube to Bob’s. Cheshire charge, while conceptually elusive, is physically genuine and readily detected in principle. Our conclusion that Wilson ...
... Our protocol for superluminal signaling is based on the observation that Wilson loop measurement causes Cheshire charge to be transferred from Alice’s flux tube to Bob’s. Cheshire charge, while conceptually elusive, is physically genuine and readily detected in principle. Our conclusion that Wilson ...
Introduction to Representations of the Canonical Commutation and
... It is natural to ask whether the commutation relations fix the operators x and D uniquely up to the unitary equivalence. If we assume that we are given two self-adjoint operators x and D acting irreducibly on a Hilbert space and satisfying (3), then the answer is positive, as proven by Stone and von ...
... It is natural to ask whether the commutation relations fix the operators x and D uniquely up to the unitary equivalence. If we assume that we are given two self-adjoint operators x and D acting irreducibly on a Hilbert space and satisfying (3), then the answer is positive, as proven by Stone and von ...
Full text in PDF form
... A symbolic mathematical representation of quantum states in terms of wave vectors and/or density operators is expected to provide an experimentally verifiable ”information” about the system. To obtain a catalogue of the corresponding statistical predictions, an a priori choice of suitable observable ...
... A symbolic mathematical representation of quantum states in terms of wave vectors and/or density operators is expected to provide an experimentally verifiable ”information” about the system. To obtain a catalogue of the corresponding statistical predictions, an a priori choice of suitable observable ...
Path Integrals — Elementary Properties and Simple Solutions
... The Trotter formula implies that the commutator term X̂ proportional to ǫ2 does not contribute in the limit N → ∞. The mathematical conditions ensuring this require functional analysis too technical to be presented here (for details, see the literature quoted at the end of the chapter). For us it is ...
... The Trotter formula implies that the commutator term X̂ proportional to ǫ2 does not contribute in the limit N → ∞. The mathematical conditions ensuring this require functional analysis too technical to be presented here (for details, see the literature quoted at the end of the chapter). For us it is ...
The Computational Complexity of Linear Optics
... causing any collapse of complexity classes or other disastrous theoretical consequences. Also, of course, there are subexponential-time factoring algorithms (such as the number field sieve), and few would express confidence that they cannot be further improved. And thus, ever since Bernstein and Vaz ...
... causing any collapse of complexity classes or other disastrous theoretical consequences. Also, of course, there are subexponential-time factoring algorithms (such as the number field sieve), and few would express confidence that they cannot be further improved. And thus, ever since Bernstein and Vaz ...
Interacting Fock spaces: central limit theorems and quantum
... 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 on the standard IFS, that is called preservation operator and computing the m ...
... 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 on the standard IFS, that is called preservation operator and computing the m ...
The Philosophy behind Quantum Gravity
... Bohr actually agreed that the measurement apparatus can also be described by quantum theory. However, he writes (1939, p. 104): ...in each case some ultimate measuring instruments, like the scales and clocks which determine the frame of space-time coordination –on which, in the last resort, even the ...
... Bohr actually agreed that the measurement apparatus can also be described by quantum theory. However, he writes (1939, p. 104): ...in each case some ultimate measuring instruments, like the scales and clocks which determine the frame of space-time coordination –on which, in the last resort, even the ...