Classical spin variables and classical counterpart of the Dirac-Feynman-Gell-Mann equation

1971 ◽  
Vol 4 (1) ◽  
pp. 19-32 ◽  
Author(s):  
S. Depaquit ◽  
PH. Gu�ret ◽  
J. P. Vigier
Keyword(s):  
Classical Spin ◽  
Classical Counterpart

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals Geometry of the Rabi Problem and Duality of Loops

2020 ◽  
Vol 75 (5) ◽  
pp. 381-391 ◽  
Author(s):  
Heinz-Jürgen Schmidt
Keyword(s):  
Magnetic Field ◽  
Differential Geometry ◽  
Floquet Theory ◽  
Bloch Sphere ◽  
Classical Spin ◽  
Periodic Magnetic Field

AbstractWe investigate the motion of a classical spin processing around a periodic magnetic field using Floquet theory, as well as elementary differential geometry and considering a couple of examples. Under certain conditions, the role of spin and magnetic field can be interchanged, leading to the notion of “duality of loops” on the Bloch sphere.

Elementary solution of Classical Spin-Glass models

1986 ◽  
Vol 65 (1) ◽  
pp. 53-63 ◽  
Author(s):  
J. L. van Hemmen ◽  
D. Grensing ◽  
A. Huber ◽  
R. Kühn
Keyword(s):  
Spin Glass ◽  
Elementary Solution ◽  
Classical Spin

scholarly journals Realization of a classical counterpart of a scalable design for adiabatic quantum computation

2007 ◽  
Vol 90 (2) ◽  
pp. 022501 ◽  
Author(s):  
V. Zakosarenko ◽  
N. Bondarenko ◽  
S. H. W. van der Ploeg ◽  
A. Izmalkov ◽  
S. Linzen ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Classical Counterpart ◽  
Adiabatic Quantum Computation ◽  
Scalable Design

GENERALIZED HANNAY ANGLE FOR THE MOST GENERAL TIME-DEPENDENT HARMONIC OSCILLATOR

1993 ◽  
Vol 07 (28) ◽  
pp. 4827-4840 ◽  
Author(s):  
DONALD H. KOBE ◽  
JIONGMING ZHU
Keyword(s):  
Harmonic Oscillator ◽  
Berry Phase ◽  
Time Dependent ◽  
Canonical Momentum ◽  
Gauge Invariant ◽  
Classical Counterpart ◽  
Mass Spring ◽  
Adiabatic Case ◽  
General Time ◽  
Total Angle

The most general time-dependent Hamiltonian for a harmonic oscillator is both linear and quadratic in the coordinate and the canonical momentum. It describes in general a harmonic oscillator with mass, spring “constant,” and friction (or antifriction) “constant,” all of which are time dependent, that is acted on by a time-dependent force. A generalized Hannay angle, which is gauge invariant, is defined by making a distinction between the Hamiltonian and the energy. The generalized Hannay angle is the classical counterpart of the generalized Berry phase in quantum theory. When friction is present the generalized Hannay angle is nonzero. If the Hamiltonian is (incorrectly) chosen to be the energy, the generalized Hannay angle is different. Nevertheless, in the adiabatic case the same total angle is obtained.

Correlation inequalities for some classical spin vector models

1975 ◽  
Vol 54 (6) ◽  
pp. 428-430 ◽  
Author(s):  
H. Kunz ◽  
Ch.-Ed. Pfister ◽  
P.-A. Vuillermot
Keyword(s):  
Correlation Inequalities ◽  
Spin Vector ◽  
Classical Spin

scholarly journals Quantum relativistic Toda chain at root of unity: isospectrality, modifiedQ-operator, and functional Bethe ansatz

2002 ◽  
Vol 31 (9) ◽  
pp. 513-553 ◽  
Author(s):  
Stanislav Pakuliak ◽  
Sergei Sergeev
Keyword(s):  
Bethe Ansatz ◽  
Weyl Algebra ◽  
Separation Of Variables ◽  
Toda Chain ◽  
Special Choice ◽  
Finite Dimensional Representation ◽  
Classical Counterpart ◽  
Discrete Integrable System ◽  
Root Of Unity ◽  
Finite Dimensional

We investigate anN-state spin model called quantum relativistic Toda chain and based on the unitary finite-dimensional representations of the Weyl algebra withqbeingNth primitive root of unity. Parameters of the finite-dimensional representation of the local Weyl algebra form the classical discrete integrable system. Nontrivial dynamics of the classical counterpart corresponds to isospectral transformations of the spin system. Similarity operators are constructed with the help of modified Baxter'sQ-operators. The classical counterpart of the modifiedQ-operator for the initial homogeneous spin chain is a Bäcklund transformation. This transformation creates an extra Hirota-type soliton in a parameterization of the chain structure. Special choice of values of solitonic amplitudes yields a degeneration of spin eigenstates, leading to the quantum separation of variables, or the functional Bethe ansatz. A projector to the separated eigenstates is constructed explicitly as a product of modifiedQ-operators.

scholarly journals Geometric Integrators for Classical Spin Systems

1997 ◽  
Vol 133 (1) ◽  
pp. 160-172 ◽  
Author(s):  
Jason Frank ◽  
Weizhang Huang ◽  
Benedict Leimkuhler
Keyword(s):  
Spin Systems ◽  
Classical Spin ◽  
Geometric Integrators

A New Uncertainty Analysis-Based Framework for Data-Driven Computational Mechanics

2021 ◽  
pp. 1-22
Author(s):  
Xu Guo ◽  
Zongliang Du ◽  
Chang Liu ◽  
Shan Tang
Keyword(s):  
Phase Space ◽  
Uncertainty Analysis ◽  
Distinctive Feature ◽  
Computational Mechanics ◽  
Problem Formulation ◽  
Solution Set ◽  
Data Driven ◽  
Data Set ◽  
Classical Counterpart ◽  
Single Solution

Abstract In the present paper, a new uncertainty analysis-based framework for data-driven computational mechanics (DDCM) is established. Compared with its practical classical counterpart, the distinctive feature of this framework is that uncertainty analysis is introduced into the corresponding problem formulation explicitly. Instated of only focusing on a single solution in phase space, a solution set is sought for in order to account for the influence of the multi-source uncertainties associated with the data set on the data-driven solutions. An illustrative example provided shows that the proposed framework is not only conceptually new, but also has the potential of circumventing the intrinsic numerical difficulties pertaining to the classical DDCM framework.

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