| 1. |
- Alm, Sven Erick, et al.
(författare)
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First Passage Percolation on \(\mathbb {Z}^2\) : A Simulation Study
- 2015
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Ingår i: Journal of statistical physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 161:3, s. 657-678
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Tidskriftsartikel (refereegranskat)abstract
- First passage percolation on is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage times attached to the edges. In this paper, the speed of the growth and the shape of the infected set is studied by aid of large-scale computer simulations, with focus on continuous passage time distributions. It is found that the most important quantity for determining the value of the time constant, which indicates the inverse asymptotic speed of the growth, is , where are i.i.d. passage time variables. The relation is linear for a large class of passage time distributions. Furthermore, the directional time constants are seen to be increasing when moving from the axis towards the diagonal, so that the limiting shape is contained in a circle with radius defined by the speed along the axes. The shape comes closer to the circle for distributions with larger variability.
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| 2. |
- Amini, Hamed, et al.
(författare)
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A Central Limit Theorem for Diffusion in Sparse Random Graphs
- 2023
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Ingår i: Journal of statistical physics. - : Springer. - 0022-4715 .- 1572-9613. ; 190
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Tidskriftsartikel (refereegranskat)abstract
- We consider bootstrap percolation and diffusion in sparse random graphs with fixed degrees, constructed by configuration model. Every vertex has two states: it is either active or inactive. We assume that to each vertex is assigned a nonnegative (integer) threshold. The diffusion process is initiated by a subset of vertices with threshold zero which consists of initially activated vertices, whereas every other vertex is inactive. Subsequently, in each round, if an inactive vertex with threshold theta has at least theta of its neighbours activated, then it also becomes active and remains so forever. This is repeated until no more vertices become activated. The main result of this paper provides a central limit theorem for the final size of activated vertices. Namely, under suitable assumptions on the degree and threshold distributions, we show that the final size of activated vertices has asymptotically Gaussian fluctuations.
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| 3. |
- Arkeryd, Leif, 1940, et al.
(författare)
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Bose condensates in interaction with excitations - a two-component space-dependent model close to equilibrium
- 2015
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Ingår i: Journal of statistical physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 160:1, s. 209-238
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Tidskriftsartikel (refereegranskat)abstract
- The paper considers a model for Bose gases in the so-called 'high-temperature range' below the temperature Tc, where Bose-Einstein condensation sets in.The model is of two-component type, consisting of a kinetic equation with periodic boundary conditions for the distribution function of a gas of excitations interacting with a Bose condensate, which is described by a Gross-Pitaevskii equation. Results on well-posedness and long time behaviour are proved in a H1-setting close to equilibrium.
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| 4. |
- Arkeryd, Leif, 1940, et al.
(författare)
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On a Taylor-Couette Type Bifurcation for the Stationary Nonlinear Boltzmann Equation
- 2006
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Ingår i: Journal of Statistical Physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 124:2-4, s. 401-443
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Tidskriftsartikel (refereegranskat)abstract
- This paper studies the stationary nonlinear Boltzmann equation for hard forces, in a Taylor-Couette setting between two coaxial, rotating cylinders with given indata of Maxwellian type on the cylinders. A priori L q -estimates are obtained, and used to prove a Taylor type bifurcation with isolated solutions and a hydrodynamic limit control, based on asymptotic expansions together with a rest term correction. The positivity of such solutions is also considered
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| 5. |
- Arkeryd, Leif, 1940
(författare)
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On low temperature kinetic theory; spin diffusion, Bose Einstein condensates, anyons
- 2013
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Ingår i: Journal of statistical physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 150:6, s. 1063-1979
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Tidskriftsartikel (refereegranskat)abstract
- The paper considers some typical problems for non-linear kinetic models evolving through pair-collisions at temperatures not far from absolute zero, which illustrate specifically quantum behaviours. Based on these examples, a number of differences between quantum and classical Boltzmann theory is then discussed in more general terms.
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| 6. |
- Aurell, Erik
(författare)
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Global Estimates of Errors in Quantum Computation by the Feynman-Vernon Formalism
- 2018
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Ingår i: Journal of statistical physics. - : SPRINGER. - 0022-4715 .- 1572-9613. ; 171:5, s. 745-767
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Tidskriftsartikel (refereegranskat)abstract
- The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over the histories of the qubits and of an environment, and afterward tracing out the environment. The qubit histories are taken to be paths on the two-sphere as in Klauder's coherent-state path integral of spin, and the environment is assumed to consist of harmonic oscillators initially in thermal equilibrium, and linearly coupled to to qubit operators . The environment can then be integrated out to give a Feynman-Vernon influence action coupling the forward and backward histories of the qubits. This representation allows to derive in a simple way estimates that the total error of operation of a quantum computer without error correction scales linearly with the number of qubits and the time of operation. It also allows to discuss Kitaev's toric code interacting with an environment in the same manner.
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| 7. |
- Aurell, Erik, et al.
(författare)
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Refined Second Law of Thermodynamics for Fast Random Processes
- 2012
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Ingår i: Journal of statistical physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 147:3, s. 487-505
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Tidskriftsartikel (refereegranskat)abstract
- We establish a refined version of the Second Law of Thermodynamics for Langevin stochastic processes describing mesoscopic systems driven by conservative or non-conservative forces and interacting with thermal noise. The refinement is based on the Monge-Kantorovich optimal mass transport and becomes relevant for processes far from quasi-stationary regime. General discussion is illustrated by numerical analysis of the optimal memory erasure protocol for a model for micron-size particle manipulated by optical tweezers.
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| 8. |
- Balinsky, A., et al.
(författare)
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Generalized Hardy inequality for the magnetic Dirichlet forms
- 2004
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Ingår i: Journal of statistical physics. - 0022-4715 .- 1572-9613. ; 116:4-Jan, s. 507-521
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Tidskriftsartikel (refereegranskat)abstract
- We obtain lower bounds for the magnetic Dirichlet form in dimensions d greater than or equal to 2. For d = 2 the results generalize a well known lower bound by the magnetic field strength: we replace the actual magnetic field B by an non-vanishing effective field which decays outside the support of B as dist( x, supp B)(-2). In the case d greater than or equal to 3 we establish that the magnetic form is bounded from below by the magnetic field strength, if one assumes that the field does not vanish and its direction is slowly varying.
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| 9. |
- Bermolen, Paola, et al.
(författare)
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Scaling Limits and Generic Bounds for Exploration Processes
- 2017
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Ingår i: Journal of statistical physics. - : SPRINGER. - 0022-4715 .- 1572-9613. ; 169:5, s. 989-1018
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Tidskriftsartikel (refereegranskat)abstract
- We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become blocked. Given an initial number of vertices N growing to infinity, we study statistical properties of the proportion of explored (active or blocked) nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the jamming constant, through a diffusion approximation for the exploration process which can be described as a unidimensional process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e., random sequential adsorption. As opposed to exploration processes on homogeneous random graphs, these do not allow for such a dimensional reduction. Instead we derive a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and we obtain generic bounds for the fluid limit and jamming constant: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, using coupling techinques, we give trajectorial interpretations of the generic bounds.
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| 10. |
- Bernhoff, Niclas, 1971-
(författare)
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Compactness Property of the Linearized Boltzmann Collision Operator for a Mixture of Monatomic and Polyatomic Species
- 2024
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Ingår i: Journal of statistical physics. - : Springer. - 0022-4715 .- 1572-9613. ; 191:3
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Tidskriftsartikel (refereegranskat)abstract
- The linearized Boltzmann collision operator has a central role in many important applications of the Boltzmann equation. Recently some important classical properties of the linearized collision operator for monatomic single species were extended to multicomponent monatomic gases and polyatomic single species. For multicomponent polyatomic gases, the case where the polyatomicity is modelled by a discrete internal energy variable was considered lately. Here we consider the corresponding case for a continuous internal energy variable. Compactness results, stating that the linearized operator can be decomposed into a sum of a positive multiplication operator, the collision frequency, and a compact operator, bringing e.g., self-adjointness, is extended from the classical result for monatomic single species, under reasonable assumptions on the collision kernel. With a probabilistic formulation of the collision operator as a starting point, the compactness property is shown by a decomposition, such that the terms are, or at least are uniform limits of, Hilbert-Schmidt integral operators and therefore are compact operators. Moreover, bounds on-including coercivity of-the collision frequency are obtained for hard sphere like, as well as hard potentials with cutoff like, models, from which Fredholmness of the linearized collision operator follows, as well as its domain.
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