scholarly journals Fermionic and bosonic fluctuation-dissipation theorem from a deformed AdS holographic model at finite temperature and chemical potential

2022 ◽  
Vol 82 (1) ◽  
Author(s):  
Nathan G. Caldeira ◽  
Eduardo Folco Capossoli ◽  
Carlos A. D. Zarro ◽  
Henrique Boschi-Filho
Keyword(s):  
Finite Temperature ◽  
Chemical Potential ◽  
Mean Square Displacement ◽  
De Sitter ◽  
Diffusive Regime ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Fermionic Systems ◽  
Long Time ◽  
The Mean

AbstractIn this work we study fluctuations and dissipation of a string in a deformed anti-de Sitter (AdS) space at finite temperature and density. The deformed AdS space is a charged black hole solution of the Einstein–Maxwell–Dilaton action. In this background we take into account the backreaction on the horizon function from an exponential deformation of the AdS space. From this model we compute the admittance and study the influence of the temperature and the chemical potential on it. We calculate the two-point correlations functions, and the mean square displacement for bosonic and fermionic cases, from which we obtain the short and large time approximations. For the long time, we obtain a sub-diffusive regime $$\sim \log t$$ ∼ log t . Combining the results from the admittance and the correlations functions we check the fluctuation-dissipation theorem for bosonic and fermionic systems.

Modification of charge density wave fluctuations by charge perturbations

2002 ◽  
Vol 12 (9) ◽  
pp. 77-78
Author(s):  
S. N. Artemenko
Keyword(s):  
Electric Field ◽  
Linear Response ◽  
Chemical Potential ◽  
Density Wave ◽  
Mean Field ◽  
Phase Fluctuations ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
The Mean ◽  
Field Transition

Spectral density of fluctuations of the CDW phase are calculated taking into account electric field induced by phase fluctuations. The approach based upon the fluctuation-dissipation theorem (FDT) combined with equations of linear response of the CDW conductor is used. Fluctuating electric field is found to suppress fluctuations of the phase, while fluctuations of the electric potential are sizeable. This suggests that transition from the CDW to the normal state (which is usually observed well below the mean-field transition temperature) may he provoked by fluctuations of the chemical potential, rather than by destruction of the CDW coherence between conducting chains due to phase fluctuations.

RANDOM WALKS ON KEBAB LATTICES: LOGARITHMIC DIFFUSION ON ORDERED STRUCTURES

1995 ◽  
Vol 09 (10) ◽  
pp. 601-606 ◽  
Author(s):  
D. CASSI ◽  
S. REGINA
Keyword(s):  
Random Walks ◽  
Linear Chain ◽  
Mean Square Displacement ◽  
Analytical Techniques ◽  
Mean Square ◽  
Ordered Structure ◽  
Ordered Structures ◽  
Asymptotic Expressions ◽  
Long Time ◽  
The Mean

Kebab lattices are ordered lattices obtained matching an infinite two-dimensional lattice to each point of a linear chain. Discrete time random walks on these structures are studied by analytical techniques. The exact asymptotic expressions of the mean square displacement and of the RW Green functions show an unexpected logarithmic behavior that is the first example of such kind of law on an ordered structure. Moreover the probability of returning to the origin shows the fastest long time decay ever found for recursive random walks.

Velocity and displacement correlation functions for fractional generalized Langevin equations

2012 ◽  
Vol 15 (3) ◽  
Author(s):  
Trifce Sandev ◽  
Ralf Metzler ◽  
Živorad Tomovski
Keyword(s):  
Initial Conditions ◽  
Mean Square Displacement ◽  
Langevin Equations ◽  
Average Particle ◽  
Mean Square ◽  
Relaxation Functions ◽  
Long Time ◽  
The Mean ◽  
Diffusive Processes ◽  
Frictional Memory Kernel

AbstractWe study analytically a generalized fractional Langevin equation. General formulas for calculation of variances and the mean square displacement are derived. Cases with a three parameter Mittag-Leffler frictional memory kernel are considered. Exact results in terms of the Mittag-Leffler type functions for the relaxation functions, average velocity and average particle displacement are obtained. The mean square displacement and variances are investigated analytically. Asymptotic behaviors of the particle in the short and long time limit are found. The model considered in this paper may be used for modeling anomalous diffusive processes in complex media including phenomena similar to single file diffusion or possible generalizations thereof. We show the importance of the initial conditions on the anomalous diffusive behavior of the particle.

Intracrystalline Transport Barriers Affecting the Self-Diffusion of CH4 in Zeolites |Na12|-A and |Na12-xKx|-A

2018 ◽  
Author(s):  
Niklas Hedin ◽  
Przemyslaw Rzepka ◽  
Alma Jasso-Salcedo ◽  
Tamara L. Church ◽  
Diana Bernin
Keyword(s):  
Close Contact ◽  
Mean Square Displacement ◽  
Diffusion Time ◽  
Mean Square ◽  
Zeolite A ◽  
Self Diffusion ◽  
Transport Barriers ◽  
Long Time ◽  
The Mean ◽  
Short Time

<p>Removing carbon dioxide is important for the upgrading of biogas or natural gas into compressed or liquefied methane, and adsorption-driven separation of CO<sub>2</sub> could be further advanced by developing for example new adsorbents. Zeolite adsorbents can select CO<sub>2</sub> over CH<sub>4</sub>, and we here confirmed that the adsorption of CH<sub>4</sub> on zeolite |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A was significantly lower for samples with a high K<sup>+</sup> content, i.e. <i>x</i> > 2. Nevertheless, these samples adsorb CH<sub>4</sub> after long equilibration times as determined with <sup>1</sup>H NMR experiments. To assess further the intracrystalline diffusion of CH<sub>4</sub> in these zeolites, pulsed-field gradient NMR experiments were performed. In large crystals of zeolites |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A, the long-time diffusion coefficients of CH<sub>4</sub> did not vary with <i>x</i>, and the mean square displacement was about 1.5 mm irrespective of the diffusion time. Also for zeolite |Na<sub>12</sub>|-A samples of three different particle sizes (~0.44, ~2.9, ~10.6 mm), the mean-square displacement of CH<sub>4</sub> was 1.5 mm and largely independent of the diffusion time. This similarity provided further evidence for an intracrystalline diffusion restriction for CH<sub>4</sub> within the medium- and large-sized zeolite A crystals, and possibly of clustering and close contact among the small zeolite A crystals. The long-time diffusion coefficient of adsorbed CH<sub>4</sub> was (at 1 atm and 298 K) about 1 ´ 10<sup>–10</sup> m<sup>2</sup>/s irrespective of the size of the zeolite particle or the studied content of K<sup>+</sup> in zeolites |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A and |Na<sub>12</sub>|-A. The <i>T</i><sub>1</sub><i> </i>relaxation time for adsorbed CH<sub>4</sub> on zeolites |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A with <i>x</i> > 2 was smaller than for those with <i>x</i> < 2, indicating that the short-time diffusion of CH<sub>4</sub> was hindered.</p>

Intracrystalline Transport Barriers Affecting the Self-Diffusion of CH4 in Zeolites |Na12|-A and |Na12-xKx|-A

2018 ◽  
Author(s):  
Niklas Hedin ◽  
Przemyslaw Rzepka ◽  
Alma Jasso-Salcedo ◽  
Tamara L. Church ◽  
Diana Bernin
Keyword(s):  
Close Contact ◽  
Mean Square Displacement ◽  
Diffusion Time ◽  
Mean Square ◽  
Zeolite A ◽  
Self Diffusion ◽  
Transport Barriers ◽  
Long Time ◽  
The Mean ◽  
Short Time

<p>Removing carbon dioxide is important for the upgrading of biogas or natural gas into compressed or liquefied methane, and adsorption-driven separation of CO<sub>2</sub> could be further advanced by developing for example new adsorbents. Zeolite adsorbents can select CO<sub>2</sub> over CH<sub>4</sub>, and we here confirmed that the adsorption of CH<sub>4</sub> on zeolite |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A was significantly lower for samples with a high K<sup>+</sup> content, i.e. <i>x</i> > 2. Nevertheless, these samples adsorb CH<sub>4</sub> after long equilibration times as determined with <sup>1</sup>H NMR experiments. To assess further the intracrystalline diffusion of CH<sub>4</sub> in these zeolites, pulsed-field gradient NMR experiments were performed. In large crystals of zeolites |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A, the long-time diffusion coefficients of CH<sub>4</sub> did not vary with <i>x</i>, and the mean square displacement was about 1.5 mm irrespective of the diffusion time. Also for zeolite |Na<sub>12</sub>|-A samples of three different particle sizes (~0.44, ~2.9, ~10.6 mm), the mean-square displacement of CH<sub>4</sub> was 1.5 mm and largely independent of the diffusion time. This similarity provided further evidence for an intracrystalline diffusion restriction for CH<sub>4</sub> within the medium- and large-sized zeolite A crystals, and possibly of clustering and close contact among the small zeolite A crystals. The long-time diffusion coefficient of adsorbed CH<sub>4</sub> was (at 1 atm and 298 K) about 1 ´ 10<sup>–10</sup> m<sup>2</sup>/s irrespective of the size of the zeolite particle or the studied content of K<sup>+</sup> in zeolites |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A and |Na<sub>12</sub>|-A. The <i>T</i><sub>1</sub><i> </i>relaxation time for adsorbed CH<sub>4</sub> on zeolites |Na<sub>12-<i>x</i></sub>K<i><sub>x</sub></i>|-A with <i>x</i> > 2 was smaller than for those with <i>x</i> < 2, indicating that the short-time diffusion of CH<sub>4</sub> was hindered.</p>

scholarly journals Identifying short- and long-time modes of the mean-square displacement: An improved nonlinear fitting approach

AIP Advances ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 055112
Author(s):  
M. K. Riahi ◽  
I. A. Qattan ◽  
J. Hassan ◽  
D. Homouz
Keyword(s):  
Mean Square Displacement ◽  
Mean Square ◽  
Nonlinear Fitting ◽  
Long Time ◽  
The Mean
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