Method for determining properties of microinstabilities of a magnetized plasma

Study comprises a determination of the plasma density at which absolute density becomes predominant by using the dielectric properties at this incipient unstable state. Relationships between wavelength, frequency, and density microinstabilities are used to derive the spatial dielectric function

The diocotron instability in a quasi-toroidal geometry

Slipstream instability of low density electron beams in crossed electric and magnetic field

Absolute and convective microinstabilities of a magnetized plasma

Absolute and convective microinstabilities of hot, fully ionized, collisionless magnetized plasm

Generalized Phase Rules

For a multi-component system, general formulas are derived for the dimension of a coexisting region in the phase diagram in various state spaces.Comment: In the revised manuscript, physical meanings of D's are explained by adding three figures. 10 pages, 3 figure

Macroscopic entanglement of many-magnon states

We study macroscopic entanglement of various pure states of a one-dimensional N-spin system with N>>1. Here, a quantum state is said to be macroscopically entangled if it is a superposition of macroscopically distinct states. To judge whether such superposition is hidden in a general state, we use an essentially unique index p: A pure state is macroscopically entangled if p=2, whereas it may be entangled but not macroscopically if p<2. This index is directly related to the stability of the state. We calculate the index p for various states in which magnons are excited with various densities and wavenumbers. We find macroscopically entangled states (p=2) as well as states with p=1. The former states are unstable in the sense that they are unstable against some local measurements. On the other hand, the latter states are stable in the senses that they are stable against local measurements and that their decoherence rates never exceed O(N) in any weak classical noises. For comparison, we also calculate the von Neumann entropy S(N) of a subsystem composed of N/2 spins as a measure of bipartite entanglement. We find that S(N) of some states with p=1 is of the same order of magnitude as the maximum value N/2. On the other hand, S(N) of the macroscopically entangled states with p=2 is as small as O(log N)<< N/2. Therefore, larger S(N) does not mean more instability. We also point out that these results are analogous to those for interacting many bosons. Furthermore, the origin of the huge entanglement, as measured either by p or S(N), is discussed to be due to the spatial propagation of magnons.Comment: 30 pages, 5 figures. The manuscript has been shortened and typos have been fixed. Data points of figures have been made larger in order to make them clearly visibl

Geometric description of BTZ black holes thermodynamics

We study the properties of the space of thermodynamic equilibrium states of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole in (2+1)-gravity. We use the formalism of geometrothermodynamics to introduce in the space of equilibrium states a $2-$dimensional thermodynamic metric whose curvature is non-vanishing, indicating the presence of thermodynamic interaction, and free of singularities, indicating the absence of phase transitions. Similar results are obtained for generalizations of the BTZ black hole which include a Chern-Simons term and a dilatonic field. Small logarithmic corrections of the entropy turn out to be represented by small corrections of the thermodynamic curvature, reinforcing the idea that thermodynamic curvature is a measure of thermodynamic interaction

Bead, Hoop, and Spring as a Classical Spontaneous Symmetry Breaking Problem

We describe a simple mechanical system that involves Spontaneous Symmetry Breaking. The system consists of two beads constrained to slide along a hoop and attached each other through a spring. When the hoop rotates about a fixed axis, the spring-beads system will change its equilibrium position as a function of the angular velocity. The system shows two different regions of symmetry separated by a critical point analogous to a second order transition. The competitive balance between the rotational diynamics and the interaction of the spring causes an Spontaneous Symmetry Breaking just as the balance between temperature and the spin interaction causes a transition in a ferromagnetic system. In addition, the gravitational potential act as an external force that causes explicit symmetry breaking and a feature of first-order transition. Near the transition point, the system exhibits a universal critical behavior where the changes of the parameter of order is described by the critical exponent beta =1/2 and the susceptibility by gamma =1. We also found a chaotic behavior near the critical point. Through a demostrative device we perform some qualitative observations that describe important features of the system.Comment: 7 pages, 2 tables, 30 figures, LaTeX2

Thermodynamic equilibrium and its stability for Microcanonical systems described by the Sharma-Taneja-Mittal entropy

It is generally assumed that the thermodynamic stability of equilibrium state is reflected by the concavity of entropy. We inquire, in the microcanonical picture, on the validity of this statement for systems described by the bi-parametric entropy $S_{_{\kappa, r}}$ of Sharma-Taneja-Mittal. We analyze the ``composability'' rule for two statistically independent systems, A and B, described by the entropy $S_{_{\kappa, r}}$ with the same set of the deformed parameters. It is shown that, in spite of the concavity of the entropy, the ``composability'' rule modifies the thermodynamic stability conditions of the equilibrium state. Depending on the values assumed by the deformed parameters, when the relation $S_{_{\kappa, r}}({\rm A}\cup{\rm B})> S_{_{\kappa, r}}({\rm A})+S_{_{\kappa, r}}({\rm B})$ holds (super-additive systems), the concavity conditions does imply the thermodynamics stability. Otherwise, when the relation $S_{_{\kappa, r}}({\rm A}\cup{\rm B})<S_{_{\kappa, r}}({\rm A})+S_{_{\kappa, r}}({\rm B})$ holds (sub-additive systems), the concavity conditions does not imply the thermodynamical stability of the equilibrium state.Comment: 13 pages, two columns, 1 figure, RevTex4, version accepted on PR

Effective Free Energy for Individual Dynamics

Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual difference is one of the main obstacles one has to overcome in order to characterize analytically economic models. In this paper, we build both on statistical mechanics and the game theory notion of Potential Function to introduce a rigorous generalization of the physicist's free energy, which includes individual dynamics. Our approach paves the way to analytical treatments of a wide range of socio-economic models and might bring new insights into them. As first examples, we derive solutions for a congestion model and a residential segregation model.Comment: 8 pages, 2 figures, presented at the ECCS'10 conferenc