scholarly journals A quantum analog of the Poincare-Birkhoff-Witt theorem

1999 ◽  
Vol 38 (4) ◽  
pp. 259-276 ◽  
Author(s):  
V. K. Kharchenko
Keyword(s):  
Quantum Analog

scholarly journals Quantum Euler Relation for Local Measurements

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 889
Author(s):  
Akram Touil ◽  
Kevin Weber ◽  
Sebastian Deffner
Keyword(s):  
Quantum Systems ◽  
Quantum Measurements ◽  
Weak Coupling Regime ◽  
Local Quantum ◽  
Dissipation Model ◽  
Local Measurements ◽  
Euler Relation ◽  
Quantum Analog ◽  
Back Action ◽  
Classical Thermodynamics

In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to account for the effects of the measurement back action. To this end, we derive a quantum analog of the Euler relation, which is governed by the information retrieved by local quantum measurements. The validity of the relation is demonstrated for the collective dissipation model, where we find that thermodynamic behavior is exhibited in the weak-coupling regime.

NONEXISTENCE OF QUANTUM NAMBU MECHANICS

1994 ◽  
Vol 09 (29) ◽  
pp. 2727-2732 ◽  
Author(s):  
DEBENDRANATH SAHOO ◽  
M. C. VALSAKUMAR
Keyword(s):  
Phase Space ◽  
Classical Mechanics ◽  
Nambu Mechanics ◽  
Quantum Analog

We investigate the problem of quantization of Nambu mechanics — a problem posed by Nambu [Phys. Rev.D7, 2405 (1973)] — along the line of Wigner–Weyl–Moyal (WWM) phase-space quantization of classical mechanics and show that the quantum analog of Nambu mechanics does not exist.

scholarly journals Probing the topology of the quantum analog of a classical skyrmion

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
O. M. Sotnikov ◽  
V. V. Mazurenko ◽  
J. Colbois ◽  
F. Mila ◽  
M. I. Katsnelson ◽  
...  
Keyword(s):  
Quantum Analog

INVESTIGATION OF THE QUANTUM CHAOS OF INTERNAL ROTATIONAL MOTION IN POLYATOMIC MOLECULES

2007 ◽  
Vol 21 (07) ◽  
pp. 415-430 ◽  
Author(s):  
A. UGULAVA ◽  
L. CHOTORLISHVILI ◽  
T. GVARJALADZE ◽  
S. CHKHAIDZE
Keyword(s):  
Experimental Observation ◽  
Rotational Motion ◽  
Quantum Chaos ◽  
Phase Plane ◽  
Torsional Oscillation ◽  
Polyatomic Molecules ◽  
Classical Dynamic ◽  
Radio Frequency Field ◽  
Dynamic Stochasticity ◽  
Quantum Analog

Polyatomic molecules can perform internal rotational motion of two types: torsional oscillation and free rotation of one part of the molecule with respect to the other part. On the phase plane, these two types of motion are separated by the separatrix. Phase trajectories, originated as a result of periodical external force action on the system, have stochastic nature. For quantum consideration, regarding the motion near to the classical separatrix, transition from the pure quantum-mechanical state to the mixed one takes place. Originating at that mixed state, this must be considered as the quantum analog of the classical dynamic stochasticity and is named as the quantum chaos. This work is devoted to the investigation of the quantum chaos manifestation in the polyatomic molecules, which have a property that performs internal rotation. For the molecule of ethane C 2 H 6, the emergence of quantum chaos and possible ways of its experimental observation has been studied. It is shown that radio-frequency field can produce the non-direct transitions between rotational and oscillatory states. These transitions, being the sign of the existence of quantum chaos, are able to change population levels sizeably. Due to this phenomenon, experimental observation of the infrared absorption is possible.

scholarly journals The Feynman–Kac Representation and Dobrushin–Lanford–Ruelle States of a Quantum Bose-Gas

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1683
Author(s):  
Yuri Suhov ◽  
Mark Kelbert ◽  
Izabella Stuhl
Keyword(s):  
Boundary Condition ◽  
Particle System ◽  
Quantum Particle ◽  
Hard Core ◽  
Infinite Volume ◽  
Quantum Gas ◽  
Finite Range ◽  
System A ◽  
Energy Part ◽  
Quantum Analog

This paper focuses on infinite-volume bosonic states for a quantum particle system (a quantum gas) in Rd. The kinetic energy part of the Hamiltonian is the standard Laplacian (with a boundary condition at the border of a ‘box’). The particles interact with each other through a two-body finite-range potential depending on the distance between them and featuring a hard core of diameter a>0. We introduce a class of so-called FK-DLR functionals containing all limiting Gibbs states of the system. As a justification of this concept, we prove that for d=2, any FK-DLR functional is shift-invariant, regardless of whether it is unique or not. This yields a quantum analog of results previously achieved by Richthammer.

Quantum vernam cipher

2002 ◽  
Vol 2 (1) ◽  
pp. 14-34
Author(s):  
D. W. Leung
Keyword(s):  
Secret Sharing ◽  
Secure Communication ◽  
Quantum Secret Sharing ◽  
Message Authentication ◽  
Classical Communication ◽  
Transmission Errors ◽  
Cipher Text ◽  
Secret Communication ◽  
Quantum Analog

We discuss aspects of secure quantum communication by proposing and analyzing a quantum analog of the Vernam cipher (one-time-pad). The quantum Vernam cipher uses entanglement as the key to encrypt quantum information sent through an insecure quantum channel. First, in sharp contrast with the classical Vernam cipher, the quantum key can be recycled securely. We show that key recycling is intrinsic to the quantum cipher-text, rather than using entanglement as the key. Second, the scheme detects and corrects for arbitrary transmission errors, and it does so using only local operations and classical communication (LOCC) between the sender and the receiver. The application to quantum message authentication is discussed. Quantum secret sharing schemes with similar properties are characterized. We also discuss two general issues, the relation between secret communication and secret sharing, the classification of secure communication protocols.

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