Product Operator - Vanderbilt Center for Structural Biology
... In Section 2 we discuss the relation of product operators to vector models and density operator theory. In the following three sections, we develop the nomenclature of product operators, the relationship between operators and vector pictures, and the rules for the evolution under shifts, couplings a ...
... In Section 2 we discuss the relation of product operators to vector models and density operator theory. In the following three sections, we develop the nomenclature of product operators, the relationship between operators and vector pictures, and the rules for the evolution under shifts, couplings a ...
Invitation to Local Quantum Physics
... The Bisognano-Wichmann Theorem The PCT theorem was used by J. Bisognano and E. Wichmann in 1976 to derive a structural result that is of fundamental importance for the application of Tomita-Takesaki modular theory in relativistic quantum field theory. Let W be a space-like wedge in space-time, i.e. ...
... The Bisognano-Wichmann Theorem The PCT theorem was used by J. Bisognano and E. Wichmann in 1976 to derive a structural result that is of fundamental importance for the application of Tomita-Takesaki modular theory in relativistic quantum field theory. Let W be a space-like wedge in space-time, i.e. ...
Projective Measurements
... basis states • Let us check what we have learned by means of a simple example • Basis vectors ...
... basis states • Let us check what we have learned by means of a simple example • Basis vectors ...
Weyl--Heisenberg Representations in Communication Theory
... The theoretical description of the communication in time–varying environments is of central relevance for further increase of the efficiency and the data rate of future transmission techniques. In particular, the quasi–statistical assumption widely used for mobile wireless communication channels is ...
... The theoretical description of the communication in time–varying environments is of central relevance for further increase of the efficiency and the data rate of future transmission techniques. In particular, the quasi–statistical assumption widely used for mobile wireless communication channels is ...
Physical Entanglement in Permutation
... which permutation-invariance is not imposed); and (ii) as about GMW-entanglement, as applied to “indistinguishable” quantum systems. The biconditionals under (i) are well-known (the first is a Theorem due to Gisin 1991); under (ii) they are not known. Proving the first biconditional under construal ...
... which permutation-invariance is not imposed); and (ii) as about GMW-entanglement, as applied to “indistinguishable” quantum systems. The biconditionals under (i) are well-known (the first is a Theorem due to Gisin 1991); under (ii) they are not known. Proving the first biconditional under construal ...
Exactly Solvable Problems in Quantum Mechanics
... solvability can be explained and derived in terms of hidden symmetry. However, even if it were true, it would probably not mean unifying all the ways to approach the problem. In fact, although many methods are based on symmetry, or – to be more specific – on the properties of Lie algebras, and altho ...
... solvability can be explained and derived in terms of hidden symmetry. However, even if it were true, it would probably not mean unifying all the ways to approach the problem. In fact, although many methods are based on symmetry, or – to be more specific – on the properties of Lie algebras, and altho ...
Entanglement Entropy
... incoherent superposition of states, it cannot be represented by any single state of which it is composed, contradicting the assumption made at the beginning. In these cases, that is when the lack of information about a collection of single states prevents us from describing them one by one complete ...
... incoherent superposition of states, it cannot be represented by any single state of which it is composed, contradicting the assumption made at the beginning. In these cases, that is when the lack of information about a collection of single states prevents us from describing them one by one complete ...
Markov property in non-commutative probability
... the strong subadditivity of the von Neumann entropy is tightly related to the Markov property invented by L. Accardi. A state of a three-fold tensor product system is Markovian if and only if it takes the equality of the strong subadditivity of von Neumann entropy, which is referred to as strong add ...
... the strong subadditivity of the von Neumann entropy is tightly related to the Markov property invented by L. Accardi. A state of a three-fold tensor product system is Markovian if and only if it takes the equality of the strong subadditivity of von Neumann entropy, which is referred to as strong add ...
L z
... • Lx , Ly and Lz don’t commute! • By Heisenberg, we can’t measure them simultaneously, so we can’t know exactly where and what L is! ...
... • Lx , Ly and Lz don’t commute! • By Heisenberg, we can’t measure them simultaneously, so we can’t know exactly where and what L is! ...
Quantum Mathematics Table of Contents
... in direct analogy with the correspondence between geometric optics and wave optics — the prototype of wave/particle duality — have straightforwardly written down the equations of “wave mechanics”, and thus anticipated quantum mechanics by almost a century. However, the lack of any physical motivatio ...
... in direct analogy with the correspondence between geometric optics and wave optics — the prototype of wave/particle duality — have straightforwardly written down the equations of “wave mechanics”, and thus anticipated quantum mechanics by almost a century. However, the lack of any physical motivatio ...
slides on Quantum Isometry Groups
... general, however, Q may fail to have a universal object. We discussed in [3] some sufficient conditions, such as the existence of a suitable cyclic separating eigenvector of D, to ensure that a universal object exists in Q0 . In general, we do get a universal object in suitable subcategories by fixi ...
... general, however, Q may fail to have a universal object. We discussed in [3] some sufficient conditions, such as the existence of a suitable cyclic separating eigenvector of D, to ensure that a universal object exists in Q0 . In general, we do get a universal object in suitable subcategories by fixi ...
1 Introduction to quantum mechanics
... 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 calculate all the properties of the system. The simpl ...
... 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 calculate all the properties of the system. The simpl ...
letter
... 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-, y- and z-directions. In quantum mechanics, there are operators which represent these three components of the angular momentum. Nuclear spins also have angular momen ...
... 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-, y- and z-directions. In quantum mechanics, there are operators which represent these three components of the angular momentum. Nuclear spins also have angular momen ...
Quantum nature of laser light
... with (1), or being identically zero in each term if we take the matrix elements of (2). Just as (1) is what we would write if we knew the laser field was prepared in a coherent state, but have no information about its phase, expression (2) is what would write if we knew that the field was prepared i ...
... with (1), or being identically zero in each term if we take the matrix elements of (2). Just as (1) is what we would write if we knew the laser field was prepared in a coherent state, but have no information about its phase, expression (2) is what would write if we knew that the field was prepared i ...
Operator Algebras and Index Theorems in Quantum Field Theory
... Relation to black hole entropy. I. Microscopic derivation of black hole entropy and its relation to conformal symmetries and central charge is discussed Strominger, Vafa and others. We illustrate our discussion by the work of Carlip. Yet we use here only the value of the central charge and not Cardy ...
... Relation to black hole entropy. I. Microscopic derivation of black hole entropy and its relation to conformal symmetries and central charge is discussed Strominger, Vafa and others. We illustrate our discussion by the work of Carlip. Yet we use here only the value of the central charge and not Cardy ...
(4)
... Often situations arise where it is appropriate to study composite dynamical systems with interacting quantum mechanical and classical degrees of freedom. In condensed matter physics such situations occur when one is interested in the dynamics of a light quantum particle or set of quantum degrees of ...
... Often situations arise where it is appropriate to study composite dynamical systems with interacting quantum mechanical and classical degrees of freedom. In condensed matter physics such situations occur when one is interested in the dynamics of a light quantum particle or set of quantum degrees of ...
Entanglement Criteria for Continuous
... harmonic oscillator systems are extremely important. A remarkable characteristic property of this system is that it has discrete energy levels which are equally spaced [10]. Thus, to explore its properties, it is best to use the energy eigenstates as the basis. Also it is convenient to assign a nonn ...
... harmonic oscillator systems are extremely important. A remarkable characteristic property of this system is that it has discrete energy levels which are equally spaced [10]. Thus, to explore its properties, it is best to use the energy eigenstates as the basis. Also it is convenient to assign a nonn ...