Time-dependent invariants of motion for complete sets of non-commuting observables

Sarris, C. M.; Proto, A. N.

doi:10.1016/j.physa.2004.09.038

Cited by 9 publications

(5 citation statements)

References 14 publications

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“…, N. They obey the generalized uncertainty relations [77] (−1) m L 2m ≥ N/2 2m−1 . Similar invariants and their special cases in the physics of particle and optical beams were considered, e.g., in the papers [78][79][80][81][82][83][84][85][86][87][88][89][90][91][92]. Such constructions are frequently used in quantum information theory under the name "symplectic invariants" [9,93,94].…”

Section: Discussionmentioning

confidence: 99%

Invariant Quantum States of Quadratic Hamiltonians

Dodonov

2021

Entropy

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Section: Discussionmentioning

confidence: 99%

Invariant Quantum States of Quadratic Hamiltonians

Dodonov

2021

Entropy

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“…"Dynamical invariants" are quantities that remain constant, but are explicit functions of time-dependent parameters and of (implicitly time-dependent) expectation values; for the harmonic oscillator, the first such invariant was noted by Lewis [20]. Korsch and Koshual used dynamical algebras to derive the dynamical invariants which lie within the algebra [21,22] (i.e., invariants which are linear in the expectation values of the algebra's operators), and Sarris and Proto demonstrated that for our state (Equation 2) it is possible to generalize further and derive dynamical invariants that are outside the algebra [23], consisting of higher powers of the the algebra's expectation values (they actually consider maximum entropy states,ρ = exp n λ n (t)L n , but a product form and exponential sum are interchangeable (see [24], corollary to theorem 2)). One such invariant in our case was found to be [25] …”

Section: Internal Frictionmentioning

confidence: 95%

Reflections on Friction in Quantum Mechanics

Rezek

2010

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Distinctly quantum friction effects of three types are surveyed: internal friction, measurement-induced friction, and quantum-fluctuation-induced friction. We demonstrate that external driving will lead to quantum internal friction, and critique the measurement-based interpretation of friction. We conclude that in general systems will experience internal and external quantum friction over and beyond the classical frictional contributions. Keywords: quantum friction; dissipation; open systemClassification: PACS 03. 05.70.Ln Friction is the price for moving too fast. An attempt to induce a rapid change in the state of a system would be accompanied by additional entropy generation and will be encumbered by energy costs. As an example of friction we can consider a body moving rapidly against a stationary background. Its kinetic energy is dissipated, generating heat and entropy in the environment. The amount of dissipation is proportional to the velocity. Another archtypical case of friction is a driven gas compression process. For a system that is thermally decoupled from its environment, rapid changes in the piston position that compresses the gas will result in internal heating of the gas and entropy generation. To restore the system to its slow quasi-static compression equivalent, heat has to be removed from the gas. This additional heat is equivalent to extra work against friction.Friction is typically modeled by a phenomenological theory within classical mechanics. How does it extend to the quantum domain? Can a first principles model of friction be developed? There are ample examples of quantum frictional phenomena. These include friction observed in micro-mechanical systems at low temperatures [1], in superfluid theory [2], and even in quantum cosmology [3] and more. Are such quantum examples of friction essentially classical phenomena that endure into the quantum

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“…On the other side, the closure Equation (17) enables us to obtain the following commutation relations [34] ( )…”

Section: Invariants Associated To the Anti-symmetry Of Matrix Gmentioning

confidence: 99%

“…Proposition 1: If a set of operators, which fulfills the commutation relation, Equation (57), closes a commutation algebra with a Hamiltonian of the type given by Equation (58), then the semiquantum matrix ( ) , G q p of the system, defined by means of the closure condition, Equation (17), is an anti-symmetric one [34].…”

Section: The Su(2) Lie Algebra Invariantsmentioning

confidence: 99%

“…(64) Note that Equations (59), (61) and (63) give rise to anti-symmetric ( ) G q matrices given by Equations (60), (62) and (64), they all exhibit the dynamic invariants given by Equations (48) to (55). Particularly, the dynamic invariants given by Equations (53), (54) and (55) adopts the forms respectively [3] [34] ( ) ( )…”

Section: The Su(2) Lie Algebra Invariantsmentioning

confidence: 99%

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