Related papers: Comment on "Phase Transition-Like Behavior in a Lo…

A generalization of the definition of a one-dimensional improper integral with a finite limit is presented. The new definition extends the range of valid integrals to include integrals which were previously considered to not be integrable.…

Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are…

Many observables in quantum field theory can be expressed in terms of trans-series, in which one adds to the perturbative series a typically infinite sum of exponentially small corrections, due to instantons or to renormalons. Even after…

It is shown how simple assumptions lead to piecewise linear behavior, which is observed in certain phase transitions.

Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurrent set can be steered to any other in that set. The…

We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on…

We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…

We study precursors of thermal phase transitions in finite systems of interacting Bose gases. For weakly repulsive interactions there is a phase transition to the one-vortex state. The distribution of zeros of the partition function…

Arrays of nanostructures have emerged as exceptional tools for the manipulation and control of light. Oftentimes, despite the fact that real implementations of nanostructure arrays must be finite, these systems are modeled as perfectly…

We study limit cycles of nonlinear oscillators described by the equation $\ddot x + \nu F(\dot x) + x =0$. Depending on the nonlinearity this equation may exhibit different number of limit cycles. We show that limit cycles correspond to…

Fluctuations may govern the fate of an interacting particle system even on the mean-field level. This is demonstrated via a three species cyclic trapping reaction with a large, yet finite number of particles, where the final number of…

Finding the equivalent resistance of an infinite ladder circuit is a classical problem in physics. We expand this well-known challenge to new classes of network topologies, in which the unit cells are much more entangled together. The exact…

In program semantics and verification, reasoning about loops is complicated by the need to produce two separate mathematical arguments: an invariant, for functional properties (ignoring termination); and a variant, for termination (ignoring…

We provide an exact mapping between the density functional of a binary mixture and that of the effective one-component fluid in the limit of infinite asymmetry. The fluid of parallel hard cubes is thus mapped onto that of parallel adhesive…

The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…

Landau theory relates phase transitions to the minimization of the Landau functional (e.g., free energy functional), which is expressed as a power series of the order parameter. It has been shown that the critical behavior of certain…

The mechanical force from light -- radiation pressure -- provides an intrinsic nonlinear interaction. Consequently, optomechanical systems near their steady state, such as the canonical optical spring, can display non-analytic behavior as a…

Complex absorbing potentials are frequently imposed when simulating unbound quantum systems. While this is usually done solely in order to avoid artifacts at the numerical boundary, we show how absorbers may also be used to probe the…

We present a classification scheme for phase transitions in finite systems like atomic and molecular clusters based on the Lee-Yang zeros in the complex temperature plane. In the limit of infinite particle numbers the scheme reduces to the…

Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…