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Exactly Solvable Problems in Quantum Mechanics
Exactly Solvable Problems in Quantum Mechanics

propagation methods for quantum molecular dynamics
propagation methods for quantum molecular dynamics

... approach, the action of the operator 6 (i.e. the mappinggenerated by the operator, ~b = 6~) is handled effectively. Local operators in coordinate space, such as the potential, are calculated on the grid points while nonlocal operators, such as the kinetic energy operator, are calculated in the funct ...
A Noncommutative Sigma Model by Mauritz van den Worm
A Noncommutative Sigma Model by Mauritz van den Worm

COHERENT STATES FOR CONTINUOUS SPECTRUM AS
COHERENT STATES FOR CONTINUOUS SPECTRUM AS

... mathematical physics, signal theory and quantum information [1 - 4]. Among the various kind of CSs, a privileged place is occupied by the generalized hypergeometric coherent states (GH-CSs), introduced in [5] and applied to the mixed (thermal) states in [6]. Moreover, the calculations involving CSs ...
THE TRIANGLE INEQUALITY AND THE DUAL GROMOV
THE TRIANGLE INEQUALITY AND THE DUAL GROMOV

... construction in [12], and thus provides a satisfactory answer to a long standing challenge. The proof of the triangle inequality which we present strengthen our understanding of our dual propinquity, provides a much more effective tool for both the theoretical study of our metric and for its applica ...
Quantum Stein`s lemma revisited, inequalities for quantum entropies
Quantum Stein`s lemma revisited, inequalities for quantum entropies

ABSTRACT ADIABATIC QUANTUM COMPUTATION: NOISE IN THE ADIABATIC THEOREM AND USING THE JORDAN-WIGNER
ABSTRACT ADIABATIC QUANTUM COMPUTATION: NOISE IN THE ADIABATIC THEOREM AND USING THE JORDAN-WIGNER

Spectral Properties of Schrödinger Operators
Spectral Properties of Schrödinger Operators

Derandomizing the Ahlswede-Winter matrix-valued Chernoff bound using pessimistic estimators, and applications
Derandomizing the Ahlswede-Winter matrix-valued Chernoff bound using pessimistic estimators, and applications

Lecture notes - UCSD Department of Physics
Lecture notes - UCSD Department of Physics

Parametrized discrete phase-space functions
Parametrized discrete phase-space functions

... Using discrete displacement-operator expansion, s-parametrized phase-space functions associated with the operators in a finite-dimensional Hilbert space are introduced and their properties are studied. In particular, the phase-space functions associated with the density operator can be regarded as q ...
Deformation Quantization and Geometric Quantization of Abelian
Deformation Quantization and Geometric Quantization of Abelian

The reduced Hamiltonian for next-to-leading-order spin
The reduced Hamiltonian for next-to-leading-order spin

A note on the realignment criterion
A note on the realignment criterion

... but f` (s1 , . . . , sm2 ) > B` (m, n). Therefore, the bound B` (m, n) can be used to detect entanglement for which the realignment criterion fails. Numerical estimations for these bounds were given for (m, n) = (2, 2) and (2, 3) in [10]. The numerical results also suggest that B̃` (2, 2) = B` (2, 2 ...
Giovannini, D., Romero, J., Leach, J., Dudley, A, Forbes, A, and
Giovannini, D., Romero, J., Leach, J., Dudley, A, Forbes, A, and

... method is that MUBs need to be defined for the small Hilbert spaces of the subsystems rather than for the large space of the overall system. This becomes especially relevant where the definition or measurement of MUBs for the overall system is challenging. We illustrate this approach by implementing ...
Monte Carlo Simulations of Quantum Spin Models - cond
Monte Carlo Simulations of Quantum Spin Models - cond

... which has an unconstrained configuration space. Only a subset of configurations of the twodimensional Ising model are allowed to occur also in the effective classical model for Z. These configurations are those that correspond to continuous, unbroken world lines. In higher spatial dimensions, one ca ...
Constructions and Noise Threshold of Topological Subsystem Codes
Constructions and Noise Threshold of Topological Subsystem Codes

Semi-classical formula beyond the Ehrenfest time in
Semi-classical formula beyond the Ehrenfest time in

An edge index for the Quantum Spin-Hall effect
An edge index for the Quantum Spin-Hall effect

... write the edge Hamiltonian as a continuous direct sum of Bloch Hamiltonians Hk . As illustrated in Fig. 2, the spectrum of each Hk consists of upper and lower continuum parts plus two nondegenerate (excepting k=0), discrete eigenvalues. These discrete eigenvalues for different k’s assemble themselve ...
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L. Fortunato - INFN Padova
L. Fortunato - INFN Padova

The Fourier grid Hamiltonian method for bound state eigenvalues and eigenfunctions c.
The Fourier grid Hamiltonian method for bound state eigenvalues and eigenfunctions c.

an extended propositional logic
an extended propositional logic

Quantum Mechanical Addition of Angular Momenta and Spin
Quantum Mechanical Addition of Angular Momenta and Spin

Derivation of the Lindblad Equation for Open Quantum Systems and
Derivation of the Lindblad Equation for Open Quantum Systems and

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Compact operator on Hilbert space

In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite-rank operators in the uniform operator topology. As such, results from matrix theory can sometimes be extended to compact operators using similar arguments. In contrast, the study of general operators on infinite-dimensional spaces often requires a genuinely different approach.For example, the spectral theory of compact operators on Banach spaces takes a form that is very similar to the Jordan canonical form of matrices. In the context of Hilbert spaces, a square matrix is unitarily diagonalizable if and only if it is normal. A corresponding result holds for normal compact operators on Hilbert spaces. (More generally, the compactness assumption can be dropped. But, as stated above, the techniques used are less routine.)This article will discuss a few results for compact operators on Hilbert space, starting with general properties before considering subclasses of compact operators.
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