Engineering the accurate distortion of an object's temperature-distribution signature

It is up to now a challenge to control the conduction of heat. Here we develop a method to distort the temperature distribution signature of an object at will. As a result, the object accurately exhibits the same temperature distribution signature as another object that is predetermined, but actually does not exist in the system. Our finite element simulations confirm the desired effect for different objects with various geometries and compositions. The underlying mechanism lies in the effects of thermal metamaterials designed by using this method. Our work is of value for applications in thermal engineering.Comment: 11 pages, 4 figure

Critical behaviours of contact near phase transitions

A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears in universal relations among thermodynamic quantities, such as large momentum tails, energy, and dynamic structure factors, through the renowned Tan relations. However, a conceptual question remains open as to whether or not contact can signify phase transitions that are insensitive to short-range physics. Here we show that, near a continuous classical or quantum phase transition, contact exhibits a variety of critical behaviors, including scaling laws and critical exponents that are uniquely determined by the universality class of the phase transition and a constant contact per particle. We also use a prototypical exactly solvable model to demonstrate these critical behaviors in one-dimensional strongly interacting fermions. Our work establishes an intrinsic connection between the universality of dilute many-body systems and universal critical phenomena near a phase transition.Comment: Final version published in Nat. Commun. 5:5140 doi: 10.1038/ncomms6140 (2014

Perturbation theory of von Neumann Entropy

In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the dimension is infinite. We develop the perturbation theory systematically for calculating von Neumann entropy of non-degenerate systems as well as degenerate systems. The result turns out to be a practical way of the expansion calculation of von Neumann entropy.Comment: 7 page

Proof of a Conjecture of Hirschhorn and Sellers on Overpartitions

Let $\bar{p}(n)$ denote the number of overpartitions of $n$. It was conjectured by Hirschhorn and Sellers that \bar{p}(40n+35)\equiv 0\ ({\rm mod\} 40) for $n\geq 0$. Employing 2-dissection formulas of quotients of theta functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating function for $\bar{p}(40n+35)$ modulo 5. Using the $(p, k)$-parametrization of theta functions given by Alaca, Alaca and Williams, we give a proof of the congruence \bar{p}(40n+35)\equiv 0\ ({\rm mod\} 5). Combining this congruence and the congruence \bar{p}(4n+3)\equiv 0\ ({\rm mod\} 8) obtained by Hirschhorn and Sellers, and Fortin, Jacob and Mathieu, we give a proof of the conjecture of Hirschhorn and Sellers.Comment: 11 page