Quantum dissipation

Celeghini, E.; Rasetti, Mario; Vitiello, Giuseppe

doi:10.1016/0003-4916(92)90302-3

Cited by 238 publications

(422 citation statements)

References 13 publications

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“…It is well known, for example, that in thermal field theory the doubled degrees of freedom describe the heat bath [7,[11][12][13][14][15]; or, near a black hole, such a doubling describes the modes on the two sides of the horizon [16][17][18].…”

Section: The Doubling Of the Degrees Of Freedommentioning

confidence: 99%

“…Coordinate doubling has also entered into the canonical quantization of dissipative systems [15,26,27] and it appears to be intimately related to the algebraic properties of the theory [10,12,13,28], as I will discuss below.…”

Section: The Doubling Of the Degrees Of Freedommentioning

confidence: 99%

“…H is the Hamiltonian responsible for the time variation in the explicit time dependence of A(t, θ(t)). H + Q can be therefore identified with the free energy [15]: variations in time of the deformation parameter involve dissipation. In thermal theories and in dissipative systems the doubled modes B play the role of the thermal bath or environment.…”

Section: −Iȧ(t θ(T)) = −I δ δT A(t θ(T)) − I δθ δT δ δθ A(t θ(T)) mentioning

confidence: 99%

“…In the infinite volume limit, the number of degrees of freedom becomes uncountable infinite, hence one obtains [7,11,15] …”

Section: −Iȧ(t θ(T)) = −I δ δT A(t θ(T)) − I δθ δT δ δθ A(t θ(T)) mentioning

confidence: 99%

“…In this limit, the "points" of the space H ≡ {H θ , ∀θ} of the infinitely many uir of the ccr are labelled by the deformation parameter θ [12,13,15].…”

Section: −Iȧ(t θ(T)) = −I δ δT A(t θ(T)) − I δθ δT δ δθ A(t θ(T)) mentioning

confidence: 99%

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Classical trajectories and quantum field theory

Vitiello¹

2005

Braz. J. Phys.

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The density matrix and the Wigner function formalism requires the doubling of the degrees of freedom in quantum mechanics (QM) and quantum field theory (QFT). The doubled degrees of freedom play the role of the thermal bath or environment degrees of freedom and are entangled with the system degrees of freedom. They also account for quantum noise in the fluctuating random forces in the system-environment coupling. The algebraic structure of QFT turns out to be the one of the deformed Hopf algebra. In such a frame, the trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations turn out to be classical trajectories and, under convenient conditions, they may exhibit properties typical of classical chaotic trajectories in nonlinear dynamics. The quantum Brownian motion and the two-slit experiment in QM are discussed in connection with the doubling of the degrees of freedom.

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Section: The Doubling Of the Degrees Of Freedommentioning

confidence: 99%

Section: The Doubling Of the Degrees Of Freedommentioning

confidence: 99%

Section: −Iȧ(t θ(T)) = −I δ δT A(t θ(T)) − I δθ δT δ δθ A(t θ(T)) mentioning

confidence: 99%

“…In the infinite volume limit, the number of degrees of freedom becomes uncountable infinite, hence one obtains [7,11,15] …”

Section: −Iȧ(t θ(T)) = −I δ δT A(t θ(T)) − I δθ δT δ δθ A(t θ(T)) mentioning

confidence: 99%

“…In this limit, the "points" of the space H ≡ {H θ , ∀θ} of the infinitely many uir of the ccr are labelled by the deformation parameter θ [12,13,15].…”

Section: −Iȧ(t θ(T)) = −I δ δT A(t θ(T)) − I δθ δT δ δθ A(t θ(T)) mentioning

confidence: 99%

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Classical trajectories and quantum field theory

Vitiello¹

2005

Braz. J. Phys.

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Quantum Dissipation and Quantum Noise

1995

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We derive the exact action for a damped mechanical system ( and the special case of the linear oscillator) from the path integral formulation of the quantum Brownian motion problem developed by Schwinger and by Feynman and Vernon. The doubling of the phase-space degrees of freedom for dissipative systems and thermal field theories is discussed and the initial values of the doubled variables are related to quantum noise effects.

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Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics

et al. 1995

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By resorting to the Fock-Bargmann representation, we incorporate the quantum Weyl-Heisenberg algebra, q-WH, into the theory of entire analytic functions. The q-WH algebra operators are realized in terms of finite difference operators in the z plane. In order to exhibit the relevance of our study, several applications to different cases of physical interest are discussed: squeezed states and the relation between coherent states and theta functions on one side, lattice quantum mechanics and Bloch functions on the other, are shown to find a deeper mathematical understanding in terms of q-WH. The rôle played by the finite difference operators and the relevance of the lattice structure in the completeness of the coherent states system suggest that the quantization of the WH algebra is an essential tool in the physics of discretized (periodic) systems.

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Quantum dissipation

Cited by 238 publications

References 13 publications

Classical trajectories and quantum field theory

Classical trajectories and quantum field theory

Quantum Dissipation and Quantum Noise

Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics

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