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Phase space methods in finite quantum systems.Hadhrami, Hilal Al January 2009 (has links)
Quantum systems with finite Hilbert space where position x and momentum
p take values in Z(d) (integers modulo d) are considered. Symplectic tranformations
S(2¿,Z(p)) in ¿-partite finite quantum systems are studied and
constructed explicitly. Examples of applying such simple method is given
for the case of bi-partite and tri-partite systems. The quantum correlations
between the sub-systems after applying these transformations are discussed
and quantified using various methods. An extended phase-space x¿p¿X¿P
where X, P ¿ Z(d) are position increment and momentum increment, is introduced.
In this phase space the extended Wigner and Weyl functions are
defined and their marginal properties are studied. The fourth order interference
in the extended phase space is studied and verified using the extended
Wigner function. It is seen that for both pure and mixed states the fourth
order interference can be obtained. / Ministry of Higher Education, Sultanate of Oman
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Vortices in Josephson arrays interacting with non-classical microwaves: The effect of dissipation.Konstadopoulou, Anastasia, Hollingworth, J.M., Everitt, M., Vourdas, Apostolos, Clark, T.D., Ralph, J.F. January 2003 (has links)
No / Vortices circulating in a ring made from a Josephson array in the insulating phase are studied. The ring contains a `dual Josephson junction' through which the vortices tunnel. External non-classical microwaves are coupled to the device. The time evolution of this two-mode fully quantum mechanical system is studied, taking into account the dissipation in the system. The effect of the quantum statistics of the photons on the quantum statistics of the vortices is discussed. Entropic calculations quantify the entanglement between the two systems. Quantum phenomena in the system are also studied through Wigner functions. After a certain time (which depends on the dissipation parameters) these quantum phenomena are destroyed due to dissipation.
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Covariant Weyl quantization, symbolic calculus, and the product formulaGunturk, Kamil Serkan 16 August 2006 (has links)
A covariant Wigner-Weyl quantization formalism on the manifold that uses
pseudo-differential operators is proposed. The asymptotic product formula that leads
to the symbol calculus in the presence of gauge and gravitational fields is presented.
The new definition is used to get covariant differential operators from momentum
polynomial symbols. A covariant Wigner function is defined and shown to give
gauge-invariant results for the Landau problem. An example of the covariant Wigner
function on the 2-sphere is also included.
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Operador Deslocamento Condicional: Geração de Estados e Medida da Função de Wigner / Conditional Operator Shift: Generation of states and the Wigner Function MeasureSOUZA, Simone Ferreira 24 March 2006 (has links)
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Previous issue date: 2006-03-24 / We present a feasible proposal for the construction of the conditional displacement operator
using a Kerr medium between two beam splitters fed from coherent states
highly excited. The device allows the implementation of the generation of a new class of states
the quantized electromagnetic field (arbitrary superpositions of states with states
moved) and the measurement of the Wigner function for arbitrary states. The application
special case of the number of states and study their nonclassical properties were
also considered. / Apresentamos uma proposta factível para a construção do operador deslocamento condicional
usando um meio Kerr entre dois divisores de feixes alimentados por estados coerentes
altamente excitados. O dispositivo permite implementar a geração de uma nova classe de estados
do campo eletromagnético quantizado (superposições de estados arbitrários com estados
deslocados) bem como a medição da função de Wigner para estados arbitrários. A aplicação
especial ao caso de estados de número e o estudo de suas propriedades não-clássicas, foram
também consideradas.
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Bi-fractional transforms in phase spaceAgyo, Sanfo David January 2016 (has links)
The displacement operator is related to the displaced parity operator through a two dimensional Fourier transform. Both operators are important operators in phase space and the trace of both with respect to the density operator gives the Wigner functions (displaced parity operator) and Weyl functions (displacement operator). The generalisation of the parity-displacement operator relationship considered here is called the bi-fractional displacement operator, O(α, β; θα, θβ). Additionally, the bi-fractional displacement operators lead to the novel concept of bi-fractional coherent states. The generalisation from Fourier transform to fractional Fourier transform can be applied to other phase space functions. The case of the Wigner-Weyl function is considered and a generalisation is given, which is called the bi-fractional Wigner functions, H(α, β; θα, θβ). Furthermore, the Q−function and P−function are also generalised to give the bi-fractional Q−functions and bi-fractional P−functions respectively. The generalisation is likewise applied to the Moyal star product and Berezin formalism for products of non-commutating operators. These are called the bi-fractional Moyal star product and bi-fractional Berezin formalism. Finally, analysis, applications and implications of these bi-fractional transforms to the Heisenberg uncertainty principle, photon statistics and future applications are discussed.
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Bi-fractional transforms in phase spaceAgyo, Sanfo D. January 2016 (has links)
The displacement operator is related to the displaced parity operator through a two dimensional
Fourier transform. Both operators are important operators in phase space
and the trace of both with respect to the density operator gives the Wigner functions
(displaced parity operator) and Weyl functions (displacement operator). The generalisation
of the parity-displacement operator relationship considered here is called
the bi-fractional displacement operator, O(α, β; θα, θβ). Additionally, the bi-fractional
displacement operators lead to the novel concept of bi-fractional coherent states.
The generalisation from Fourier transform to fractional Fourier transform can be
applied to other phase space functions. The case of the Wigner-Weyl function is considered
and a generalisation is given, which is called the bi-fractional Wigner functions,
H(α, β; θα, θβ). Furthermore, the Q−function and P−function are also generalised to
give the bi-fractional Q−functions and bi-fractional P−functions respectively. The
generalisation is likewise applied to the Moyal star product and Berezin formalism for
products of non-commutating operators. These are called the bi-fractional Moyal star
product and bi-fractional Berezin formalism.
Finally, analysis, applications and implications of these bi-fractional transforms
to the Heisenberg uncertainty principle, photon statistics and future applications are
discussed.
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