The work of our group on reproducing scenarios of high energy theoretical physics on Dirac materials, like graphene, is illustrated. The main goal of this paper is to explain how versatile these systems are, and how far and wide into the hep-th territory we can explore with them. I first review why these materials lend themselves to the emergence of special relativistic-like matter and space, with the focus on the emergence of curvature. Then the crucial role of the low dimensions (2+1), and Weyl symmetry, towards the realization of a Unruh-kind of phenomenon (along with other interesting scenarios, that include the BTZ black hole and de Sitter spacetime) is explained. Comments on how far we went in the direction of experiments are offered too, followed by a list of some fresh results: From the time-loop to spot torsion, to the generalized uncertainty principle stemming from and underlying (lattice) length; From a model of grain-boundaries and their relation to (A)dS and Poincaré spacetime algebras, to Unconventional Supersymmetry and the role of the two Dirac points of graphene; and more. In the concluding remarks I briefly try to make the case for the realization of a ``CERN for analogs'', where theorists. both of the hep-th and of the cond-mat types, sit next to experimentalists, mostly of the cond-mat type.

Background: Many attempts have been made to resolve in time the folding of model proteins in computer simulations. Different computational approaches have emerged. Some of these approaches suffer from the insensitivity to the geometrical properties of the proteins (lattice models), while others are computationally heavy (traditional MD). Results: We use a recently-proposed approach of Zhou and Karplus to study the folding of the protein model based on the discrete time molecular dynamics algorithm. We show that this algorithm resolves with respect to time the folding --- unfolding transition. In addition, we demonstrate the ability to study the coreof the model protein. Conclusion: The algorithm along with the model of inter-residue interactions can serve as a tool to study the thermodynamics and kinetics of protein models.

We demonstrate that the recently proposed pruned-enriched Rosenbluth method PERM (P.~Grassberger, Phys.~Rev.~{\bf E 56} (1997) 3682) leads to very efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and, thus, allows to analyze static aspects of the folding behavior of arbitrary sequences.

We discuss recent theoretical developments in the study of simple lattice models of proteins. Such models are designed to understand general features of protein structures and mechanism of folding. Among the topics covered are (i) the use of lattice models to understand the selection of the limited set of viable protein folds; (ii) the relationship between structure and sequence spaces; (iii) the application of lattice models for studying folding mechanisms (topological frustration, kinetic partitioning mechanism). Classification of folding scenarios based on the intrinsic thermodynamic properties of a sequence (namely, the collapse and folding transition temperatures) is outlined. A brief discussion of random heteropolymer model is also presented.

We show that arguments in the comment by Schwab et al. quant-ph/0503018 on our recent work are invalid.

This paper is a comment to M Wilkinson, EPL 106 (2014) 40001, arXiv:1401.4620 [physics.ao-ph,cond-mat.soft], which draws conclusion from our data that are at variance with our observations.

We discuss the problem of Poincare recurrences in area-preserving maps and the universality of their decay at long times. The work is related to to the results presented in Refs. [1,2].

Different aspects of protein folding are illustrated by simplified polymer models. Stressing the diversity of side chains (residues) leads one to view folding as the freezing transition of an heteropolymer. Technically, the most common approach to diversity is randomness, which is usually implemented in two body interactions (charges, polar character,..). On the other hand, the (almost) universal character of the protein backbone suggests that folding may also be viewed as the crystallization transition of an homopolymeric chain, the main ingredients of which are the peptide bond and chirality (proline and glycine notwithstanding). The model of a chiral dipolar chain leads to a unified picture of secondary structures, and to a possible connection of protein structures with ferroelectric domain theory.

We consider equilibrium folding transitions in lattice protein models with and without side chains. A dimensionless measure, $Omega_{c}$, is introduced to quantitatively assess the degree of cooperativity in lattice models and in real proteins. We show that larger values of $Ω_{c}$ resembling those seen in proteins are obtained in lattice models with side chains (LMSC). The enhanced cooperativity in LMSC is due to the possibility of denser packing of side chains in the interior of the model protein. We also establish that $Ω_{c}$ correlates extremely well with (σ= (T_θ -T_{f} )/T_θ), where (T_θ) and (T_{f}) are collapse and folding transition temperatures, respectively. These theoretical ideas are used to analyze folding transitions in various real proteins. The values of $Ω_{c}$ extracted from experiments show a correlation with $σ$. We conclude that the degree of cooperativity can be expressed in terms of the single parameter $σ$, which can be estimated from experimental data.

The folding kinetics of a number of sequences for off-lattice continuum model of proteins is studied using Langevin simulations at two values of the friction coefficient. We show that there is a remarkable correlation between folding times, $τ_{F}$, and $σ= (T_{θ} - T_{F})/T_{θ} $, where $T_{θ}$ and $T_{F}$ are the equilibrium collapse and folding transition temperatures, respectively. The microscopic dynamics reveals several scenarios for the refolding kinetics depending on the values of $σ$. Proteins with small $σ$ reach the native conformation via a nucleation collapse mechanism and their energy landscape is characterized by single dominant native basin of attraction. Proteins with large $σ$ get trapped in competing basins of attraction, in which they adopt misfolded structures. In this case only a small fraction of molecules $Φ$ access the native state rapidly, the majority of them approach the native state by a three stage multipathway mechanism. The partition factor $Φ$ is determined by $σ$: smaller the value of $σ$ larger is $Φ$. The qualitative aspects of our results are found to be independent of the friction coefficient. Estimates for time scales for folding of small proteins via a nucleation collapse mechanism are presented.