scholarly journals Semiclassical Strings in (2+1)-Dimensional Backgrounds

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Sergio Giardino
Keyword(s):  
Space Time ◽  
Quantum Model ◽  
Quantum Oscillations ◽  
Free Particles ◽  
Classical Quantum ◽  
Geometrical Relationship

This study analyzes the geometrical relationship between a classical string and its semiclassical quantum model. From an arbitrary (2+1)-dimensional geometry, a specific ansatz for a classical string is used to generate a semi-classical quantum model. In this framework, examples of quantum oscillations and quantum free particles are presented that uniquely determine a classical string and the space-time geometry where its motion takes place.

scholarly journals A contribution to modern ideas on the quantum theory

1927 ◽  
Vol 115 (770) ◽  
pp. 208-214
Keyword(s):  
Quantum Theory ◽  
Kinetic Energy ◽  
Line Element ◽  
Natural Extension ◽  
Space Time ◽  
Relativity Theory ◽  
Unit Mass ◽  
The World ◽  
Free Particles ◽  
Theory Of Gravitation

The relativity theory of gravitation indicates that space-time is a four dimensional continuum in which the line element is measured by the equation ( ds ) 2 = g mn dx m dx n , (1) the notation being that generally adopted. The world-lines or natural tracks of free particles in this space are geodesics. From (1) we have g mn dx m /ds . dx n /ds = 1, (2) the quantity on the left being an expression corresponding to the kinetic energy of ordinary dynamics for a particle of unit mass. This correspondence is readily appreciated if it be noted that dx m /ds is the natural extension of the velocity, dx m /dt .

Motion of Free Particles in Fractal Space-time

2009 ◽  
Vol 10 (11-12) ◽  
Author(s):  
C. Gh. Buzea ◽  
C. Bejinariu ◽  
C. Boris ◽  
P. Vizureanu ◽  
M. Agop
Keyword(s):  
Space Time ◽  
Free Particles ◽  
Fractal Space

scholarly journals ON THE OCCURRENCE OF A POSITIVE VACUUM ENERGY IN A QUANTUM MODEL FOR SPACE–TIME

1999 ◽  
Vol 14 (31) ◽  
pp. 2169-2177
Author(s):  
GEORGE CHAPLINE
Keyword(s):  
Vacuum Energy ◽  
Dimensional Space ◽  
String Tension ◽  
Space Time ◽  
Accelerating Universe ◽  
Quantum Model ◽  
Observational Constraints ◽  
Discrete Form ◽  
Dimensional Space Time ◽  
New Type

It is shown that a previously proposed quantum model for four-dimensional space–time based on an SU (∞) generalization of anyonic superconductivity can be regarded as a discrete form of Polyakov's string theory. This suggests that in a Robertson–Walker universe there is a positive vacuum energy that is on the order of the string tension divided by square of the distance scale factor. This leads to a new type of cosmological model that, even though it resembles more an open universe than an accelerating universe, is apparently consistent with current observational constraints on cosmological models.

QUANTUM MODEL FOR SPACE-TIME

1992 ◽  
Vol 07 (22) ◽  
pp. 1959-1965 ◽  
Author(s):  
GEORGE CHAPLINE
Keyword(s):  
Mathematical Model ◽  
Wave Function ◽  
Coherent State ◽  
Quantum State ◽  
Three Dimensional ◽  
Space Time ◽  
Quantum Model ◽  
Observable Universe ◽  
Pure Quantum State ◽  
First Time

It is suggested that a recently constructed condensate wave function for a three-dimensional anyonic superfluid can be reinterpreted as a coherent state for gravitons. This wave function provides for the first time a mathematical model showing how macroscopic space-time might emerge from microscopic fluctuations in topology, and suggests that the observable universe may be in a nearly pure quantum state.

scholarly journals Hybrid Classical-Quantum Fitting Attention States to Statistical Mechanics of Neocortical Interactions

2021 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Statistical Mechanics ◽  
Multiple Scales ◽  
Wave Packets ◽  
Quantum Systems ◽  
Quantum Model ◽  
Quantum Processes ◽  
Multivariate Statistical ◽  
Synaptic Interactions ◽  
Classical Quantum ◽  
Random Shocks

Hybrid Classical-Quantum computing has already arrived at several commercial quantum computers, offered to researchers and businesses. Here, application is made to a classical-quantum model of human neocortex, Statistical Mechanics of Neocortical Interactions (SMNI), which has had its applications published in many papers since 1981. However, this project only uses Classical (super-)computers. Since 2015, a path-integral algorithm, PATHINT, used previously to accurately describe several systems in several disciplines, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space described by SMNI applies nonlinear nonequilibrium multivariate statistical mechanics to synaptic neuronal interactions, while the quantum space described by qPATHINT applies synaptic contributions from Ca2+ waves generated by astrocytes at tripartite neuron-astrocyte-neuron sites. Previous SMNI publications since 2013 have calculated the astrocyte Ca2+ wave synaptic interactions from a closed-form (analytic) expression derived by the Principal Investigator (PI). However, more realistic random shocks to the Ca2+ waves from ions entering and leaving these wave packets should be included using qPATHINT between electroencephalographic (EEG) measurements which decohere the quantum wave packets. This current project extends calculations to multiple scales of interaction between classical events and expectations over the Ca2+ quantum processes to include these random shocks in previous codes used to fit EEG data to the SMNI model, that included the analytic forms for the quantum processes but now replaced by qPATHINT. The PI's Adaptive Simulated Annealing (ASA) importance-sampling optimization code is used for fitting the combined classical-quantum system. Gaussian Quadratures is used for numerical calculation of momenta expectations of the astrocyte processes that contribute to SMNI synaptic interactions. This project thereby demonstrates how some hybrid classical-quantum systems may be calculated quite well using only classical (super-)computers.

scholarly journals Anisotropic Heisenberg model for the mixed spin-3/2 and spin-1/2 under random crystal field

2021 ◽  
Vol 24 (1) ◽  
pp. 13704
Author(s):  
D. Sabi Takou ◽  
M. Karimou ◽  
F. Hontinfinde ◽  
E. Albayrak
Keyword(s):  
Crystal Field ◽  
Heisenberg Model ◽  
Classical Case ◽  
Absolute Temperature ◽  
Quantum Model ◽  
Mixed Spin ◽  
Wide Range ◽  
Classical Quantum ◽  
Oguchi Approximation ◽  
Qualitative Changes

Thermodynamic properties of the mixed spin-3/2 and spin-1/2 Heisenberg model are examined within the Oguchi approximation in the presence of a random crystal-field (RCF). The RCF is either introduced with probability p or turned off with probability 1-p randomly. The thermal variations of the global magnetization and free energy of the system are investigated to construct the phase diagrams for the classical, quantum and anisotropic cases. Different results revealed that no qualitative changes exist between them. Quantum effects are found to be present and abundant in the quantum model in the negative D -range. This phenomenon has a strong decreasing effect on the critical temperature which becomes much lower than in the classical case. In the presence of an external field, it was observed that coercivity and remanence decrease in a wide range of the absolute temperature.

scholarly journals The Quantization of a Kerr-AdS Black Hole

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Claus Gerhardt
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Quantum Gravity ◽  
Gravitational Waves ◽  
Space Time ◽  
Quantum Model ◽  
Quantum Space ◽  
Curvature Singularity ◽  
Cauchy Hypersurface ◽  
Extended Space

We apply our model of quantum gravity to a Kerr-AdS space-time of dimension2m+1,m≥2, where all rotational parameters are equal, resulting in a wave equation in a quantum space-time which has a sequence of solutions that can be expressed as a product of stationary and temporal eigenfunctions. The stationary eigenfunctions can be interpreted as radiation and the temporal ones as gravitational waves. The event horizon corresponds in the quantum model to a Cauchy hypersurface that can be crossed by causal curves in both directions such that the information paradox does not occur. We also prove that the Kerr-AdS space-time can be maximally extended by replacing in a generalized Boyer-Lindquist coordinate system thervariable byρ=r2such that the extended space-time has a timelike curvature singularity inρ=-a2.

scholarly journals The classical-quantum divergence of complexity in modelling spin chains

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 25 ◽  
Author(s):  
Whei Yeap Suen ◽  
Jayne Thompson ◽  
Andrew J. P. Garner ◽  
Vlatko Vedral ◽  
Mile Gu
Keyword(s):  
Stochastic Process ◽  
Quantum Mechanics ◽  
Complexity Science ◽  
Spin Chains ◽  
Quantum Mechanical ◽  
Quantum Model ◽  
Qualitative Behaviour ◽  
Ising Spin ◽  
Statistical Complexity ◽  
Classical Quantum

The minimal memory required to model a given stochastic process - known as the statistical complexity - is a widely adopted quantifier of structure in complexity science. Here, we ask if quantum mechanics can fundamentally change the qualitative behaviour of this measure. We study this question in the context of the classical Ising spin chain. In this system, the statistical complexity is known to grow monotonically with temperature. We evaluate the spin chain's quantum mechanical statistical complexity by explicitly constructing its provably simplest quantum model, and demonstrate that this measure exhibits drastically different behaviour: it rises to a maximum at some finite temperature then tends back towards zero for higher temperatures. This demonstrates how complexity, as captured by the amount of memory required to model a process, can exhibit radically different behaviour when quantum processing is allowed.

scholarly journals Hybrid Classical-Quantum Fitting Attention States to Statistical Mechanics of Neocortical Interactions

2021 ◽  
Author(s):  
Lester Ingber
Keyword(s):  
Statistical Mechanics ◽  
Multiple Scales ◽  
Wave Packets ◽  
Quantum Systems ◽  
Quantum Model ◽  
Quantum Processes ◽  
Multivariate Statistical ◽  
Synaptic Interactions ◽  
Classical Quantum ◽  
Random Shocks

Hybrid Classical-Quantum computing has already arrived at several commercial quantum computers, offered to researchers and businesses. Here, application is made to a classical-quantum model of human neocortex, Statistical Mechanics of Neocortical Interactions (SMNI), which has had its applications published in many papers since 1981. However, this project only uses Classical (super-)computers. Since 2015, a path-integral algorithm, PATHINT, used previously to accurately describe several systems in several disciplines, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems, qPATHINT. Published papers have described the use of qPATHINT to neocortical interactions and financial options. The classical space described by SMNI applies nonlinear nonequilibrium multivariate statistical mechanics to synaptic neuronal interactions, while the quantum space described by qPATHINT applies synaptic contributions from Ca2+ waves generated by astrocytes at tripartite neuron-astrocyte-neuron sites. Previous SMNI publications since 2013 have calculated the astrocyte Ca2+ wave synaptic interactions from a closed-form (analytic) expression derived by the Principal Investigator (PI). However, more realistic random shocks to the Ca2+ waves from ions entering and leaving these wave packets should be included using qPATHINT between electroencephalographic (EEG) measurements which decohere the quantum wave packets. This current project extends calculations to multiple scales of interaction between classical events and expectations over the Ca2+ quantum processes to include these random shocks in previous codes used to fit EEG data to the SMNI model, that included the analytic forms for the quantum processes but now replaced by qPATHINT. The PI's Adaptive Simulated Annealing (ASA) importance-sampling optimization code is used for fitting the combined classical-quantum system. Gaussian Quadratures is used for numerical calculation of momenta expectations of the astrocyte processes that contribute to SMNI synaptic interactions. This project thereby demonstrates how some hybrid classical-quantum systems may be calculated quite well using only classical (super-)computers.

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