Reconstructing Fourier's law from disorder in quantum wires

The theory of open quantum systems is used to study the local temperature and heat currents in metallic nanowires connected to leads at different temperatures. We show that for ballistic wires the local temperature is almost uniform along the wire and Fourier's law is invalid. By gradually increasing disorder, a uniform temperature gradient ensues inside the wire and the thermal current linearly relates to this local temperature gradient, in agreement with Fourier's law. Finally, we demonstrate that while disorder is responsible for the onset of Fourier's law, the non-equilibrium energy distribution function is determined solely by the heat baths

Quantum transport efficiency and Fourier's law

We analyze the steady-state energy transfer in a chain of coupled two-level systems connecting two thermal reservoirs. Through an analytic treatment we find that the energy current is independent of the system size, hence violating Fourier's law of heat conduction. The classical diffusive behavior in Fourier's law of heat conduction can be recovered by introducing decoherence to the quantum systems constituting the chain. Implications of these results on energy transfer in biological light harvesting systems, and the role of quantum coherences and entanglement are discussed.Comment: 6 pages, 4 figure

Temperature Profiles in Hamiltonian Heat Conduction

We study heat transport in the context of Hamiltonian and related stochastic models with nearest-neighbor coupling, and derive a universal law for the temperature profiles of a large class of such models. This law contains a parameter $\alpha$, and is linear only when $\alpha=1$. The value of $\alpha$ depends on energy-exchange mechanisms, including the range of motion of tracer particles and their times of flight.Comment: Revised text, same results Second revisio

Fourier's Law: insight from a simple derivation

The onset of Fourier's law in a one-dimensional quantum system is addressed via a simple model of weakly coupled quantum systems in contact with thermal baths at their edges. Using analytical arguments we show that the crossover from the ballistic (invalid Fourier's law) to diffusive (valid Fourier's law) regimes is characterized by a thermal length-scale, which is directly related to the profile of the local temperature. In the same vein, dephasing is shown to give rise to a classical Fourier's law, similarly to the onset of Ohm's law in mesoscopic conductors.Comment: 4+ pages, references and discussions adde

Thermal conductivity through the nineteenth century

As a material property and as a metaphor, thermal conductivity occupies an important position in physical, biological and geological sciences. Yet, its precise measurement is dependent on using electricity as a proxy because flowing heat cannot directly be measured.Comment: Submitted to Physics Today. 4,500 words, 4 figure

Crystal energy functions via the charge in types A and C

The Ram-Yip formula for Macdonald polynomials (at t=0) provides a statistic which we call charge. In types A and C it can be defined on tensor products of Kashiwara-Nakashima single column crystals. In this paper we prove that the charge is equal to the (negative of the) energy function on affine crystals. The algorithm for computing charge is much simpler and can be more efficiently computed than the recursive definition of energy in terms of the combinatorial R-matrix.Comment: 25 pages; 1 figur

Anarchism, Utopianism and Hospitality: The Work of René Schérer

René Schérer (born 1922) is lamentably almost unknown to the Anglo-American world as his work has, as yet, not been translated . He is one of the main specialists of the French “utopian socialist”, Charles Fourier (1772-1837), and a major thinker in his own right. He is the author of more than twenty books and co-editor of the journal Chimères. Colleague and friend at Vincennes university (Paris 8) of Michel Foucault, Gilles Deleuze, Félix Guattari, Jacques Derrida, Jacques Rancière, Jean-François Lyotard, François Châletet, Alain Brossat, Georges Navet, Miguel Abensour, Pierre Macherey… he continues to host seminars at Paris 8 (now located at St. Denis). He is a living testimony to a radical past, and a continuing inspiration to a new generation of young thinkers. This article aims to convey the original specificity of his understanding of anarchism. By so doing, it will stress the importance of his work for any thinking concerned with a politicised resistance to social conformity and the supposed “state of things” today

Electronic thermal transport in strongly correlated multilayered nanostructures

The formalism for a linear-response many-body treatment of the electronic contributions to thermal transport is developed for multilayered nanostructures. By properly determining the local heat-current operator, it is possible to show that the Jonson-Mahan theorem for the bulk can be extended to inhomogeneous problems, so the various thermal-transport coefficient integrands are related by powers of frequency (including all effects of vertex corrections when appropriate). We illustrate how to use this formalism by showing how it applies to measurements of the Peltier effect, the Seebeck effect, and the thermal conductance.Comment: 17 pages, 4 figures, submitted to Phys. Rev.

Distribution of roots of random real generalized polynomials

The average density of zeros for monic generalized polynomials, $P_n(z)=\phi(z)+\sum_{k=1}^nc_kf_k(z)$, with real holomorphic $\phi ,f_k$ and real Gaussian coefficients is expressed in terms of correlation functions of the values of the polynomial and its derivative. We obtain compact expressions for both the regular component (generated by the complex roots) and the singular one (real roots) of the average density of roots. The density of the regular component goes to zero in the vicinity of the real axis like $|\hbox{\rm Im}\,z|$. We present the low and high disorder asymptotic behaviors. Then we particularize to the large $n$ limit of the average density of complex roots of monic algebraic polynomials of the form $P_n(z) = z^n +\sum_{k=1}^{n}c_kz^{n-k}$ with real independent, identically distributed Gaussian coefficients having zero mean and dispersion $\delta = \frac 1{\sqrt{n\lambda}}$. The average density tends to a simple, {\em universal} function of $\xi={2n}{\log |z|}$ and $\lambda$ in the domain $\xi\coth \frac{\xi}{2}\ll n|\sin \arg (z)|$ where nearly all the roots are located for large $n$.Comment: 17 pages, Revtex. To appear in J. Stat. Phys. Uuencoded gz-compresed tarfile (.66MB) containing 8 Postscript figures is available by e-mail from [email protected]

Tomograms and other transforms. A unified view

A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the symplectic and affine groups is treated in some detail. Special emphasis is given to the properties of the scale-time and scale-frequency tomograms. Tomograms are interpreted as a tool to sample the signal space by a family of curves or as the matrix element of a projector.Comment: 19 pages latex, submitted to J. Phys. A: Math and Ge