A quantum phase transition (QPT) is an inherently dynamic phenomenon. However, while non-dissipative quantum dynamics is described in detail, the question, that is not thoroughly understood is how the omnipresent dissipative processes enter the critical dynamics near a quantum critical point (QCP). Here we report a general approach enabling inclusion of both adiabatic and dissipative processes ...

Supramolecular polymerization has been traditionally focused on the thermodynamic equilibrium state, where one-dimensional assemblies reside at the global minimum of the Gibbs free energy. The pathway and rate to reach the equilibrium state are irrelevant, and the resulting assemblies remain unchanged over time. In the past decade, the focus has shifted to kinetically trapped (non-dissipative n...

A necessary condition for existence of general dissipative magnetohydrodynamic equilibria is derived. The ingredients of the derivation are Ohm’s law and the existence of magnetic surfaces, only in the sense of KAM theorem. All other equations describing the system matter exclusively for the evaluation of the condition in a concrete case. PACS: 52.30.-q , 47.20.-k , 47.65.+a

In this paper, we investigate when passivity for a nonlinear system can be inferred from its linearization. The nonlinear system considered here are affine in control and with feedthrough terms, in both continuous-time domain and discrete-time domain. Our main results demonstrate when the linearized system is simultaneously strict passive and strict input passive (SSIP), the nonlinear system wi...

Granular media are dissipative systems. The collisions between the grains are inelastic and therefore energy is intrinsically lost within the system while it is in motion. In order to explore some of the fundamental resulting effects on the statistical properties of such systems, let us idealize a granular medium by a set of N spherical particles, all being identical and having only the exclusi...

We study symmetries in the design of large-scale dissipative and passive control. In the framework of dissipativity and passivity theory, stability conditions for large-scale systems are derived by categorizing agents into symmetry groups and applying local control laws under limited interconnections with neighbors. We show that there exists an upper bound on the number of subsystems that can b...

Space-time evolution and subsequent particle production from minimally viscous (η/s=0.08) QGP fluid is studied using the 2nd order Israel-Stewart’s theory of dissipative relativistic fluid. Compared to ideal fluid, energy density or temperature evolves slowly in viscous dynamics. Particle yield at high pT is increased. Elliptic flow on the other hand decreases in viscous dynamics. Minimally vis...

For a class of dissipative Schrödinger operators H = −∆ + V (x) with a complex-valued potential V = V1−iV2 with V2 ≥ 0 and |V (x)| = O(|x| ) as |x| tends to infinity, we prove that the complex eigenvalues of H can not accumulate to zero. In the perturbation regime where V2 is sufficiently small, we show under some conditions that N(V ) = N(V1)+k, where k is the multiplicity of the zero resonanc...

The lJnearized version of nonstochastic cont~nuum theory is used wJth the ngid anchonng hypothesis to study the occurrence of transient penodic dissipative structures (DS) induced m a nematic sample by a magnetic field H of supercritical strength applied m a

This work describes a classification of the N-soliton solutions of the Kadomtsev-Petviashvili II equation in terms of chord diagrams of N chords joining pairs of 2N points. The different classes of N-solitons are enumerated by the distribution of crossings of the chords. The generating function of the chord diagrams is expressed as a continued fraction, special cases of which are moment generat...