Related papers: New classical integrable systems from generalized …
A new method, dual-space cluster expansion, is proposed to study classical phases transitions in the continuum. It relies on replacing the particle positions as integration variables by the momenta of the relative displacements of particle…
Soft colloids allow to explore high density states well beyond random close packing. An important open question is whether softness controls the dynamics under these dense conditions. While experimental works reported conflicting results,…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
We develop a dynamical symmetry approach to path integrals for general interacting quantum spin systems. The time-ordered exponential obtained after the Hubbard-Stratonovich transformation can be disentangled into the product of a finite…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
We compute the Bethe equations of generalized Hubbard models, and study their thermodynamical limit. We argue how they can be connected to the ones found in the context of AdS/CFT correspondence, in particular with the so-called dressing…
In this essay, we first sketch the development of ideas on the extraordinary dynamics of integrable classical nonlinear and quantum many body Hamiltonians. In particular, we comment on the state of mathematical techniques available for…
A general semiclassical approach to quantum systems with system-bath interactions is developed. We study system decoherence in detail using a coherent state semiclassical wavepacket method which avoids singularity issues arising in the…
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…
In the context of quantum field theory (QFT), unstable particles are associated with complex-valued poles of two-body scattering matrices in the unphysical sheet of rapidity space. The Breit-Wigner formula relates this pole to the mass and…
In quantum many-body theory no generic microscopic principle at the origin of complex dynamics is known. Quite opposed, in classical mechanics the theory of non-linear dynamics provides a detailed framework for the distinction between…
Integrable systems offer rare examples of solvable many-body problems in the quantum world. Due to the fine-tuned structure, their realization in nature and experiment is never completely accurate, therefore effects of integrability are…
It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic…
Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which…
In this paper, we continue the study of $T\bar{T}$ deformation in $d=1$ quantum mechanical systems and propose possible analogues of $J\bar{T}$ deformation and deformation by a general linear combination of $T\bar{T}$ and $J\bar{T}$ in…
Spontaneous pattern formation out of homogeneous media is one of the well-understood examples of hydrodynamic instabilities in classical systems, which naturally leads to the question of its manifestation in quantum fluids. Bose-Einstein…
As is well-known, there exists a four parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum dependent terms, and we determine…
In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…
Discrete time crystals are a many-body state of matter where the extensive system's dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific properties required to demonstrate such a…
Using the kinematic constraints of classical bodies we construct the allowable wavefunctions corresponding to classical solids. These are shown to be long lived metastable states that are qualitatively far from eigenstates of the true…