how quantum logic differs from classical logic: following distribution
... a simplistic (mathematical) way, the loss of distributivity is expressed as a change from classical logic (CL) to quantum logic (QL). We follow that change within a system of axioms common to both quantum and classical logic. The system is expressed in a spatial language called Boundary Mathematics ...
... a simplistic (mathematical) way, the loss of distributivity is expressed as a change from classical logic (CL) to quantum logic (QL). We follow that change within a system of axioms common to both quantum and classical logic. The system is expressed in a spatial language called Boundary Mathematics ...
Observations on Hyperplane: II. Dynamical Variables and
... fields over extended space-time domains, it fails to come to grips with the fact that relatively moving inertial observers tend to favor different observables within a given local algebra. Each inertial observer tends to favor, for measurement, observables that approximate observables at a definite ...
... fields over extended space-time domains, it fails to come to grips with the fact that relatively moving inertial observers tend to favor different observables within a given local algebra. Each inertial observer tends to favor, for measurement, observables that approximate observables at a definite ...
Quantum Probability - Institut Camille Jordan
... We stop for a moment our list of definitions and properties and we focus on the relations between observables and usual random variables in Probability Theory. For the simplicity of the discussion we consider only the case of pure states, the general case can be easily deduced by a procedure called ...
... We stop for a moment our list of definitions and properties and we focus on the relations between observables and usual random variables in Probability Theory. For the simplicity of the discussion we consider only the case of pure states, the general case can be easily deduced by a procedure called ...
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 ...
Spectral Properties of Schrödinger Operators
... nämlich der Graphen, auf denen zwei beliebige Punkte durch einen eindeutigen Weg verbunden sind. Spektralprobleme für Laplace- und SchrödingerOperatoren auf solchen Strukturen wurden in den letzten Jahren intensiv erforscht, [15, 30, 51, 48, 63, 62, 72, 73]. In den Arbeiten [46, 26] haben wir ...
... nämlich der Graphen, auf denen zwei beliebige Punkte durch einen eindeutigen Weg verbunden sind. Spektralprobleme für Laplace- und SchrödingerOperatoren auf solchen Strukturen wurden in den letzten Jahren intensiv erforscht, [15, 30, 51, 48, 63, 62, 72, 73]. In den Arbeiten [46, 26] haben wir ...
Dilations, Poduct Systems and Weak Dilations∗
... the case of Hilbert spaces the strict topology is the ∗–σ–strong topology. It is well-known that normal representations of B(H) are also ∗–σ–strong, so for Hilbert modules the strict topology on the ball is, indeed, an appropriate substitute of the normal topology. Dilations are among the most impor ...
... the case of Hilbert spaces the strict topology is the ∗–σ–strong topology. It is well-known that normal representations of B(H) are also ∗–σ–strong, so for Hilbert modules the strict topology on the ball is, indeed, an appropriate substitute of the normal topology. Dilations are among the most impor ...
AN INDEX THEORY FOR QUANTUM DYNAMICAL SEMIGROUPS 1
... (H, F, j) is called a subordinate weak Markov flow with expectation semigroup {Tt } if H is a Hilbert space containing H0 as a subspace, F = F (t) is a non-decreasing family of orthogonal projections on H with F (0) having range H0 , and j = {jt } is a family of ∗-homomorphisms from A0 into B(H) sat ...
... (H, F, j) is called a subordinate weak Markov flow with expectation semigroup {Tt } if H is a Hilbert space containing H0 as a subspace, F = F (t) is a non-decreasing family of orthogonal projections on H with F (0) having range H0 , and j = {jt } is a family of ∗-homomorphisms from A0 into B(H) sat ...
Waxman
... By this we can see that if the phase differs in л so we can measure the field precisely but then uncertainties of other pairs of angles will increase.for the vacuum state the mean is: ...
... By this we can see that if the phase differs in л so we can measure the field precisely but then uncertainties of other pairs of angles will increase.for the vacuum state the mean is: ...
Chapter 2 Theory of angular momentum
... • In classical mechanics, a rigid object admits two kinds of angular momentum: ~ = ~r × ~p), associated with the motion of the center of mass; – orbital (L ~ = Iω), associated with the motion about the center of mass. – spin (|S| F.i., the Earth has an orbital angular momentum attributable to its an ...
... • In classical mechanics, a rigid object admits two kinds of angular momentum: ~ = ~r × ~p), associated with the motion of the center of mass; – orbital (L ~ = Iω), associated with the motion about the center of mass. – spin (|S| F.i., the Earth has an orbital angular momentum attributable to its an ...
DOC
... (different problem for each ℓ ) Power series solution (see text for details). Solutions depend on 2 quantum numbers: n and ℓ (for each effective potential ℓ = 0, 1, 2, … have a set of solutions labeled by index n.) ...
... (different problem for each ℓ ) Power series solution (see text for details). Solutions depend on 2 quantum numbers: n and ℓ (for each effective potential ℓ = 0, 1, 2, … have a set of solutions labeled by index n.) ...
Toward an Understanding of Parochial Observables
... fundamental results in the theory of C*-algebras, known as the GNS theorem (Kadison & Ringrose 1997, p. 278, Thm. 4.5.2), asserts that for each state ω on A, there exists a representation (πω , Hω ) of A, known as the GNS representation for ω, and a (cyclic) vector Ωω ∈ Hω such that for all A ∈ A, ω ...
... fundamental results in the theory of C*-algebras, known as the GNS theorem (Kadison & Ringrose 1997, p. 278, Thm. 4.5.2), asserts that for each state ω on A, there exists a representation (πω , Hω ) of A, known as the GNS representation for ω, and a (cyclic) vector Ωω ∈ Hω such that for all A ∈ A, ω ...
6 Product Operators
... perpendicular to the plane of the rotation. The x-, y- and z-components of this vector can be specified, and these are the angular momenta in the x-, yand z-directions. In quantum mechanics, there are operators which represent these three components of the angular momentum. Nuclear spins also have a ...
... perpendicular to the plane of the rotation. The x-, y- and z-components of this vector can be specified, and these are the angular momenta in the x-, yand z-directions. In quantum mechanics, there are operators which represent these three components of the angular momentum. Nuclear spins also have a ...
Loop Quantum Gravity and Its Consistency
... Another problem that is encountered is fermion doubling. It was a problem that was first encountered in Lattice Gauge Theory and extends to Loop Quantum Gravity. The mathematical origin of the problem is that, when looking at the propagator of the free Dirac theory, the introduction of lattice momen ...
... Another problem that is encountered is fermion doubling. It was a problem that was first encountered in Lattice Gauge Theory and extends to Loop Quantum Gravity. The mathematical origin of the problem is that, when looking at the propagator of the free Dirac theory, the introduction of lattice momen ...
6 Product Operators
... description of the product operator formalism. In quantum mechanics, two mathematical objects – wavefunctions and operators – are of central importance. The wavefunction describes the system of interest (such as a spin or an electron) completely; if the wavefunction is known it is possible to calcul ...
... description of the product operator formalism. In quantum mechanics, two mathematical objects – wavefunctions and operators – are of central importance. The wavefunction describes the system of interest (such as a spin or an electron) completely; if the wavefunction is known it is possible to calcul ...
Chapter 3 Basic quantum statistical mechanics of spin
... set of matrices such that no unitary transformation U S a U † block-diagonalizes all three matrices. From the theory of Lie algebras, it is known that for su(2) there is exactly one set (up to unitary transformations) of irreducible n × n matrices for each integer n. For reasons soon to be apparent, ...
... set of matrices such that no unitary transformation U S a U † block-diagonalizes all three matrices. From the theory of Lie algebras, it is known that for su(2) there is exactly one set (up to unitary transformations) of irreducible n × n matrices for each integer n. For reasons soon to be apparent, ...
Operator Quantum Error Correction.
... part of this scheme opens up the possibility of studying noiseless subsystems for arbitrary quantum operations. This paper is an expanded and more detailed version of the work [1]. We provide complete details for proofs sketched there, and in some cases we present an alternative “operator” approach ...
... part of this scheme opens up the possibility of studying noiseless subsystems for arbitrary quantum operations. This paper is an expanded and more detailed version of the work [1]. We provide complete details for proofs sketched there, and in some cases we present an alternative “operator” approach ...