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Maurizio Fagotti - One of the best experts on this subject based on the ideXlab platform.
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Quantum quenches in the transverse field Ising chain: II. Stationary State properties
Journal of Statistical Mechanics: Theory and Experiment, 2012Co-Authors: Pasquale Calabrese, Fabian H. L. Essler, Maurizio FagottiAbstract:We consider the Stationary State properties of the reduced density matrix as well as spin–spin correlation functions after a sudden quantum quench of the magnetic field in the transverse field Ising chain. We demonstrate that Stationary State properties are described by a generalized Gibbs ensemble. We discuss the approach to the Stationary State at late times.
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quantum quench in the transverse field ising chain ii Stationary State properties
arXiv: Statistical Mechanics, 2012Co-Authors: Pasquale Calabrese, Fabian H. L. Essler, Maurizio FagottiAbstract:We consider the Stationary State properties of the reduced density matrix as well as spin-spin correlation functions after a sudden quantum quench of the magnetic field in the transverse field Ising chain. We demonstrate that Stationary State properties are described by a generalized Gibbs ensemble. We discuss the approach to the Stationary State at late times.
C. Godreche - One of the best experts on this subject based on the ideXlab platform.
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Structure of the Stationary State of the asymmetric target process
Journal of Statistical Mechanics: Theory and Experiment, 2007Co-Authors: J. M. Luck, C. GodrecheAbstract:We introduce a novel migration process, the target process. This process is dual to the zero-range process (ZRP) in the sense that, while for the ZRP the rate of transfer of a particle only depends on the occupation of the departure site, it only depends on the occupation of the arrival site for the target process. More precisely, duality associates to a given ZRP a unique target process, and vice-versa. If the dynamics is symmetric, i.e., in the absence of a bias, both processes have the same Stationary-State product measure. In this work we focus our interest on the situation where the latter measure exhibits a continuous condensation transition at some finite critical density $\rho_c$, irrespective of the dimensionality. The novelty comes from the case of asymmetric dynamics, where the target process has a nontrivial fluctuating Stationary State, whose characteristics depend on the dimensionality. In one dimension, the system remains homogeneous at any finite density. An alternating scenario however prevails in the high-density regime: typical configurations consist of long alternating sequences of highly occupied and less occupied sites. The local density of the latter is equal to $\rho_c$ and their occupation distribution is critical. In dimension two and above, the asymmetric target process exhibits a phase transition at a threshold density $\rho_0$ much larger than $\rho_c$. The system is homogeneous at any density below $\rho_0$, whereas for higher densities it exhibits an extended condensate elongated along the direction of the mean current, on top of a critical background with density $\rho_c$.
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structure of the Stationary State of the asymmetric target process
Journal of Statistical Mechanics: Theory and Experiment, 2007Co-Authors: J. M. Luck, C. GodrecheAbstract:We introduce a novel migration process, the target process. This process is dual to the zero-range process (ZRP) in the sense that, while for the ZRP the rate of transfer of a particle only depends on the occupation of the departure site, it only depends on the occupation of the arrival site for the target process. More precisely, duality associates to a given ZRP a unique target process, and vice versa. If the dynamics is symmetric, i.e., in the absence of a bias, both processes have the same Stationary-State product measure. In this work we focus our interest on the situation where the latter measure exhibits a continuous condensation transition at some finite critical density ρc, irrespective of the dimensionality. The novelty comes from the case of asymmetric dynamics, where the target process has a nontrivial fluctuating Stationary State, whose characteristics depend on the dimensionality. In one dimension, the system remains homogeneous at any finite density. An alternating scenario prevails at high density: typical configurations consist of long alternating sequences of highly occupied and less occupied sites. The local density of the latter sites is equal to ρc and their occupation distribution is critical. The coherence length of these alternating structures diverges quadratically at high density. In dimension two and above, the asymmetric target process exhibits a phase transition at a threshold density ρ0 much larger than ρc. The system is homogeneous at any density below ρ0, whereas for higher densities it exhibits an extended condensate elongated along the direction of the mean current, on top of a critical background with density ρc.
Marcel Den Nijs - One of the best experts on this subject based on the ideXlab platform.
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Stationary-State skewness in two-dimensional Kardar-Parisi-Zhang type growth
Physical Review E, 1999Co-Authors: Chen-shan Chin, Marcel Den NijsAbstract:We present numerical Monte Carlo results for the Stationary State properties of KPZ type growth in two dimensional surfaces, by evaluating the finite size scaling (FSS) behaviour of the 2nd and 4th moments, $W_2$ and $W_4$, and the skewness, $W_3$, in the Kim-Kosterlitz (KK) and BCSOS model. Our results agree with the Stationary State proposed by L\"assig. The roughness exponents $W_n\sim L^{\alpha_n}$ obey power counting, $\alpha_n= n \alpha$, and the amplitude ratio's of the moments are universal. They have the same values in both models: $W_3/W_2^{1.5}= -0.27(1)$ and $W_4/W_2^{2}= +3.15(2)$. Unlike in one dimension, the Stationary State skewness is not tunable, but a universal property of the Stationary State distribution. The FSS corrections to scaling in the KK model are weak and $\alpha$ converges well to the Kim-Kosterlitz-L\"assig value $\alpha={2/5} $. The FSS corrections to scaling in the BCSOS model are strong. Naive extrapolations yield an smaller value, $\alpha\simeq 0.38(1)$, but are still consistent with $\alpha={2/5}$ if the leading irrelevant corrections to FSS scaling exponent is of order $y_{ir}\simeq -0.6(2)$.
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Stationary State Skewness in KPZ Type Growth
Journal of Physics A: Mathematical and General, 1997Co-Authors: John Neergaard, Marcel Den NijsAbstract:Stationary States in KPZ type growth have interesting short distance properties. We find that typically they are skewed and lack particle-hole symmetry. E.g., hill-tops are typically flatter than valley bottoms, and all odd moments of the height distribution function are non-zero. Stationary State skewness can be turned on and off in the 1+1 dimensional RSOS model. We construct the exact Stationary State for its master equation in a 4 dimensional parameter space. In this State steps are completely uncorrelated. Familiar models such as the Kim-Kosterlitz model lie outside this space, and their Stationary States are skewed. We demonstrate using finite size scaling that the skewness diverges with systems size, but such that the skewness operator is irrelevant in 1+1 dimensions, with an exponent $y_{sk}\simeq-1$, and that the KPZ fixed point lies at zero-skewness.
Abraham Minsky - One of the best experts on this subject based on the ideXlab platform.
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Nucleoid restructuring in Stationary‐State bacteria
Molecular microbiology, 2004Co-Authors: Daphna Frenkiel-krispin, Irit Ben-avraham, Joseph Englander, Eyal Shimoni, Sharon G. Wolf, Abraham MinskyAbstract:The textbook view of the bacterial cytoplasm as an unstructured environment has been overturned recently by studies that highlighted the extent to which non-random organization and coherent motion of intracellular components are central for bacterial life-sustaining activities. Because such a dynamic order critically depends on continuous consumption of energy, it cannot be perpetuated in starved, and hence energy-depleted, Stationary-State bacteria. Here, we show that, at the onset of the Stationary State, bacterial chromatin undergoes a massive reorganization into ordered toroidal structures through a process that is dictated by the intrinsic properties of DNA and by the ubiquitous starvation-induced DNA-binding protein Dps. As starvation proceeds, the toroidal morphology acts as a structural template that promotes the formation of DNA-Dps crystalline assemblies through epitaxial growth. Within the resulting condensed assemblies, DNA is effectively protected by means of structural sequestration. We thus conclude that the transition from bacterial active growth to Stationary phase entails a co-ordinated process, in which the energy-dependent dynamic order of the chromatin is sequentially substituted with an equilibrium crystalline order.
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nucleoid restructuring in Stationary State bacteria
Molecular Microbiology, 2004Co-Authors: Daphna Frenkielkrispin, Joseph Englander, Eyal Shimoni, Sharon G. Wolf, Irit Benavraham, Abraham MinskyAbstract:The textbook view of the bacterial cytoplasm as an unstructured environment has been overturned recently by studies that highlighted the extent to which non-random organization and coherent motion of intracellular components are central for bacterial life-sustaining activities. Because such a dynamic order critically depends on continuous consumption of energy, it cannot be perpetuated in starved, and hence energy-depleted, Stationary-State bacteria. Here, we show that, at the onset of the Stationary State, bacterial chromatin undergoes a massive reorganization into ordered toroidal structures through a process that is dictated by the intrinsic properties of DNA and by the ubiquitous starvation-induced DNA-binding protein Dps. As starvation proceeds, the toroidal morphology acts as a structural template that promotes the formation of DNA-Dps crystalline assemblies through epitaxial growth. Within the resulting condensed assemblies, DNA is effectively protected by means of structural sequestration. We thus conclude that the transition from bacterial active growth to Stationary phase entails a co-ordinated process, in which the energy-dependent dynamic order of the chromatin is sequentially substituted with an equilibrium crystalline order.
Pasquale Calabrese - One of the best experts on this subject based on the ideXlab platform.
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Quantum quenches in the transverse field Ising chain: II. Stationary State properties
Journal of Statistical Mechanics: Theory and Experiment, 2012Co-Authors: Pasquale Calabrese, Fabian H. L. Essler, Maurizio FagottiAbstract:We consider the Stationary State properties of the reduced density matrix as well as spin–spin correlation functions after a sudden quantum quench of the magnetic field in the transverse field Ising chain. We demonstrate that Stationary State properties are described by a generalized Gibbs ensemble. We discuss the approach to the Stationary State at late times.
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quantum quench in the transverse field ising chain ii Stationary State properties
arXiv: Statistical Mechanics, 2012Co-Authors: Pasquale Calabrese, Fabian H. L. Essler, Maurizio FagottiAbstract:We consider the Stationary State properties of the reduced density matrix as well as spin-spin correlation functions after a sudden quantum quench of the magnetic field in the transverse field Ising chain. We demonstrate that Stationary State properties are described by a generalized Gibbs ensemble. We discuss the approach to the Stationary State at late times.
