Tissue engineering of certain load-bearing parts of the body can be dependent on scaffold adhesion or integration with the surrounding tissue to prevent dislocation. One such area is the regeneration of the intervertebral disc (IVD). In this work, poly(N-isopropylacrylamide) (PNIPAAm) was grafted with chondroitin sulfate (CS) (PNIPAAm-g-CS) and blended with aldehyde-modified CS to generate an injectable polymer that can form covalent bonds with tissue upon contact. However, the presence of the reactive aldehyde groups can compromise the viability of encapsulated cells. Thus, liposomes were encapsulated in the blend, designed to deliver the ECM derivative, gelatin, after the polymer has adhered to tissue and reached physiological temperature. This work is based on the hypothesis that the discharge of gelatin will enhance the biocompatibility of the material by covalently reacting with, or “end-capping”, the aldehyde functionalities within the gel that did not participate in bonding with tissue upon contact. As a comparison, formulations were also created without CS aldehyde and with an alternative adhesion mediator, mucoadhesive calcium alginate particles. Gels formed from blends of PNIPAAm-g-CS and CS aldehyde exhibited increased adhesive strength compared to PNIPAAm-g-CS alone (p<0.05). However, the addition of gelatin-loaded liposomes to the blend significantly decreased the adhesive strength (p<0.05). The encapsulation of alginate microparticles within PNIPAAm-g-CS gels caused the tensile strength to increase two-fold over that of PNIPAAm-g-CS blends with CS aldehyde (p<0.05). Cytocompatibility studies indicate that formulations containing alginate particles exhibit reduced cytotoxicity over those containing CS aldehyde. Overall, the results indicated that the adhesives composed of alginate microparticles encapsulated in PNIPAAm-g-CS have the potential to serve as a scaffold for IVD regeneration.

We study level statistics in ensembles of integrable $N\times N$ matrices linear in a real parameter $x$. The matrix $H(x)$ is considered integrable if it has a prescribed number $n>1$ of linearly independent commuting partners $H^i(x)$ (integrals of motion) $\left[H(x),H^i(x)\right] = 0$, $\left[H^i(x), H^j(x)\right]$ = 0, for all $x$. In a recent work, we developed a basis-independent construction of $H(x)$ for any $n$ from which we derived the probability density function, thereby determining how to choose a typical integrable matrix from the ensemble. Here, we find that typical integrable matrices have Poisson statistics in the $N\to\infty$ limit provided $n$ scales at least as $\log{N}$; otherwise, they exhibit level repulsion. Exceptions to the Poisson case occur at isolated coupling values $x=x_0$ or when correlations are introduced between typically independent matrix parameters. However, level statistics cross over to Poisson at $ \mathcal{O}(N^{-0.5})$ deviations from these exceptions, indicating that non-Poissonian statistics characterize only subsets of measure zero in the parameter space. Furthermore, we present strong numerical evidence that ensembles of integrable matrices are stationary and ergodic with respect to nearest neighbor level statistics.Comment: 18 pages, 26 figures, discussion on number variance added; published versio

We consider energy transport in the classical Toda chain in the presence of an additional pinning potential. The pinning potential is expected to destroy the integrability of the system and an interesting question is to see the signatures of this breaking of integrability on energy transport. We investigate this by a study of the non-equilibrium steady state of the system connected to heat baths as well as the study of equilibrium correlations. Typical signatures of integrable systems are a size-independent energy current, a flat bulk temperature profile and ballistic scaling of equilibrium dynamical correlations, these results being valid in the thermodynamic limit. We find that, as expected, these properties change drastically on introducing the pinning potential in the Toda model. In particular, we find that the effect of a harmonic pinning potential is drastically smaller at low temperatures, compared to a quartic pinning potential. We explain this by noting that at low temperatures the Toda potential can be approximated by a harmonic inter-particle potential for which the addition of harmonic pinning does not destroy integrability.

We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT) -a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of integrable matrices consists of exactly N − M independent commuting N × N matrices linear in a real parameter. We first develop a rotationally invariant parameterization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, similar to the construction of Gaussian ensembles in the RMT.

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We study the collisionless dynamics of two classes of nonintegrable pairing models. One is a BCS model with separable energy-dependent interactions, the other -a 2D topological superconductor with spin-orbit coupling and a band-splitting external field. The long-time quantum quench dynamics at integrable points of these models are well understood. Namely, the squared magnitude of the time-dependent order parameter ∆(t) can either vanish (Phase I), reach a nonzero constant (Phase II), or periodically oscillate as an elliptic function (Phase III). We demonstrate that nonintegrable models too exhibit some or all of these nonequilibrium phases. Remarkably, elliptic periodic oscillations persist, even though both their amplitude and functional form change drastically with integrability breaking. Striking new phenomena accompany loss of integrability. First, an extremely long time scale emerges in the relaxation to Phase III, such that short-time numerical simulations risk erroneously classifying the asymptotic state. This time scale diverges near integrable points. Second, an entirely new Phase IV of quasiperiodic oscillations of |∆| emerges in the quantum quench phase diagrams of nonintegrable pairing models. As integrability techniques do not apply for the models we study, we develop the concept of asymptotic self-consistency and a linear stability analysis of the asymptotic phases. With the help of these new tools, we determine the phase boundaries, characterize the asymptotic state, and clarify the physical meaning of the quantum quench phase diagrams of BCS superconductors. We also propose an explanation of these diagrams in terms of bifurcation theory. CONTENTS 28 b. p + ip, II-III 28 References 29 arXiv:1812.04410v1 [cond-mat.quant-gas]

We obtain lower bounds on the inverse compressibility of systems whose Lee-Yang zeros of the grand-canonical partition function lie in the left half of the complex fugacity plane. This includes in particular systems whose zeros lie on the negative real axis such as the monomer-dimer system on a lattice. We also study the virial expansion of the pressure in powers of the density for such systems. We find no direct connection between the positivity of the virial coefficients and the negativity of the L-Y zeros, and provide examples of either one or both properties holding. An explicit calculation of the partition function of the monomer-dimer system on 2 rows shows that there are at most a finite number of negative virial coefficients in this case. * Dedicated to the memory of George Stell

We consider a mixture of a two-component Fermi gas and a single-component dipolar Bose gas in a square optical lattice and reduce it into an effective Fermi system where the Fermi-Fermi interaction includes the attractive interaction induced by the phonons of a uniform dipolar BoseEinstein condensate. Focusing on this effective Fermi system in the parameter regime that preserves the symmetry of D4, the point group of a square, we explore, within the Hartree-Fock-Bogoliubov mean-field theory, the phase competition among density wave orderings and superfluid pairings. We construct the matrix representation of the linearized gap equation in the irreducible representations of D4. We show that in the weak coupling regime, each matrix element, which is a four-dimensional (4D) integral in momentum space, can be put in a separable form involving a 1D integral, which is only a function of temperature and the chemical potential, and a pairing-specific "effective" interaction, which is an analytical function of the parameters that characterize the Fermi-Fermi interactions in our system. We analyze the critical temperatures of various competing orders as functions of different system parameters in both the absence and presence of the dipolar interaction. We find that close to half filling, the d x 2 −y 2 -wave pairing with a critical temperature in the order of a fraction of Fermi energy (at half filling) may dominate all other phases, and at a higher filling factor, the p-wave pairing with a critical temperature in the order of a hundredth of Fermi energy may emerge as a winner. We find that tuning a dipolar interaction can dramatically enhance the pairings with dxy-and g-wave symmetries but not enough for them to dominate other competing phases.