arXiv subjects

G. Téllez

Publications and source records attributed to G. Téllez.

7 recordsLinked to original sources

arXiv2018

Like-charge attraction in a one-dimensional setting: the importance of being odd

From cement cohesion to DNA condensation, a proper statistical physics treatment of systems with long range forces is important for a number of applications in physics, chemistry, and biology. We compute here the effective force between fixed charged macromolecules, screened by oppositely charged mobile ions (counterions). We treat the problem in a one dimensional configuration, that allows for interesting discussion and derivation of exact results, remaining at a level of mathematical difficulty compatible with an undergraduate course. Emphasis is put on the counter-intuitive but fundamental phenomenon of like-charge attraction, that our treatment brings for the first time to the level of undergraduate teaching. The parity of the number of counterions is shown to play a prominent role, which sheds light on the binding mechanism at work when like-charge macromolecules do attract.

cond-mat.soft↗

arXiv2017

Exact Energy Expansion of the two-dimensional Dyson Gas for Odd Values of $Γ/2$

Using the expansion on monomial functions of the Vandermonde determinant to the power $Γ=Q^2/(k_BT)$, a way to find the excess energy $U_{exc}$ of the two dimensional one component plasma 2dOCP on the hard and soft disk (or Dyson Gas) for odd values of $Γ/2$ is provided. At $Γ=2$, the current study not only corroborates the result for the particle-particle energy contribution of the Dyson gas found by Shakirov by using an alternative approach but also provides the exact $N$-finite expansion of the excess energy of the 2dOCP on the hard disk. The excess energy is fitted to an ansatz of the form $U_{exc} = K^1 N + K^2 \sqrt{N} + K^3 + K^4/N + O(1/N^2)$ to study the finite-size corrections with $K^i$ coefficients and $N$ the number of particles. In particular, the bulk term of the excess energy is in agreement with the well known result of Jancovici for the hard disk in the thermodynamic limit. Finally, an expression is found for the pair correlation function which still keeps a link with the random matrix theory via the kernel in the Ginibre Ensemble for odd values of $Γ/2$. A comparison between analytical 2-body density function and histograms obtained with Monte Carlo simulations for small systems and $Γ=2,6,10,\ldots$ shows that the approach described in this work may be used to study analytically the crossover behaviour from a disordered system to small crystals. Key words: Coulomb gas, one-component plasma, Ginibre ensemble, solvable models

cond-mat.stat-mech↗

arXiv2014

Singular Behavior At The Edge of Laughlin States

A distinguishing feature of fractional quantum Hall (FQH) states is a singular behavior of equilibrium densities at boundaries. In contrast to states at integer filling fraction, such quantum liquids posses an additional dipole moment localized near edges. It enters observable quantities such as universal dispersion of edge states and Lorentz shear stress. For a Laughlin state, this behavior is seen as a peak, or overshoot, in the single particle density near the edge, reflecting a general tendency of electrons in FQH states to cluster near edges. We compute the singular edge behavior of the one particle density by a perturbative expansion carried out around a completely filled Landau level. This correction is shown to fully capture the dipole moment and the major features of the overshoot observed numerically. Furthermore, it exhibits the Stokes phenomenon with the Stokes line at the boundary of the droplet, decaying like a Gaussian inside and outside the liquid with different decay lengths. In the limit of vanishing magnetic length the shape the overshoot is a singular double layer with a capacity that is a universal function of the filling fraction. Finally, we derive the edge dipole moment of Pfaffian FQH states. The result suggests an explicit connection between the magnitude of the dipole moment and the bulk odd viscosity.

cond-mat.str-el↗

arXiv2012

Classical and Quantum Chaos in the Diamond Shaped Billiard

We analyse the classical and quantum behaviour of a particle trapped in a diamond shaped billiard. We defined this billiard as a half stadium connected with a triangular billiard. A parameter $ξ$ which gradually change the shape of the billiard from a regular equilateral triangle ($ξ=1$) to a diamond ($ξ=0$) was used to control the transition between the regular and chaotic regimes. The classical behaviour is regular when the control parameter $ξ$ is one; in contrast, the system is chaotic when $ξ\neq 1$ even for values of $ξ$ close to one. The entropy grows fast as $ξ$ is decreased from 1 and the Lyapunov exponent remains positive for $ξ<1$. The Finite Difference Method was implemented in order to solve the quantum problem. The energy spectrum and eigenstates were numerically computed for different values of the control parameter. The nearest-neighbour spacing distribution is analysed as a function of $ξ$, finding a Poisson and a Gaussian Orthogonal Ensemble(GOE) distribution for regular and chaotic regimes respectively. Several scars and bouncing ball states are shown with their corresponding classical periodic orbits. Along the document the classical chaos identifiers are computed to show that system is chaotic. On the other hand, the quantum counterpart is in agreement with the Bohigas-Giannoni-Schmit conjecture and exhibits the standard features for chaotic billiard such as the scarring of the wavefunction.

nlin.CD↗

arXiv2012

A two-dimensional one component plasma and a test charge : polarization effects and effective potential

We study the effective interactions between a test charge Q and a one-component plasma, i.e. a complex made up of mobile point particles with charge q, and a uniform oppositely charged background. The background has the form of a flat disk, in which the mobile charges can move. The test particle is approached perpendicularly to the disk, along its axis of symmetry. All particles interact by a logarithmic potential. The long and short distance features of the effective potential --the free energy of the system for a given distance between Q and the disk-- are worked out analytically in detail. They crucially depend on the sign of Q/q, and on the global charge borne by the discotic complex, that can vanish. While most results are obtained at the intermediate coupling Gamma = beta q^2 = 2 (beta being the inverse temperature), we have also investigated situations with stronger couplings: Gamma=4 and 6. We have found that at large distances, the sign of the effective force reflects subtle details of the charge distribution on the disk, whereas at short distances, polarization effects invariably lead to effective attractions.

cond-mat.stat-mech↗

arXiv2004

Charge Fluctuations for a Coulomb Fluid in a Disk on a Pseudosphere

The classical (i.e. non-quantum) equilibrium statistical mechanics of a Coulomb fluid living on a pseudosphere (an infinite surface of constant negative curvature) is considered. The Coulomb fluid occupies a large disk communicating with a reservoir (grand-canonical ensemble). The total charge $Q$ on the disk fluctuates. In a macroscopic description, the charge correlations near the boundary circle can be described as correlations of a surface charge density $σ$. In a macroscopic approach, the variance of $Q$ and the correlation function of $σ$ are computed; they are universal. These macroscopic results are shown to be valid for two solvable microscopic models, in the limit when the microscopic thickness of the surface charge density goes to zero.

cond-mat.stat-mech↗

arXiv2003

Pressures for a One-Component Plasma on a Pseudosphere

The classical (i.e. non-quantum) equilibrium statistical mechanics of a two-dimensional one-component plasma (a system of charged point-particles embedded in a neutralizing background) living on a pseudosphere (an infinite surface of constant negative curvature) is considered. In the case of a flat space, it is known that, for a one-component plasma, there are several reasonable definitions of the pressure, and that some of them are not equivalent to each other. In the present paper, this problem is revisited in the case of a pseudosphere. General relations between the different pressures are given. At one special temperature, the model is exactly solvable in the grand canonical ensemble. The grand potential and the one-body density are calculated in a disk, and the thermodynamic limit is investigated. The general relations between the different pressures are checked on the solvable model.

cond-mat.stat-mech↗