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Register a new userDensity-correlator signatures of the vulcanization transition
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Certain density correlators, measurable via various experimental techniques, are studied in the context of the vulcanization transition. It is shown that these correlators contain essential information about both the vulcanization transition and the emergent amorphous solid state. Contact is made with various physical ingredients that have featured in experimental studies of amorphous colloidal and gel systems and in theoretical studies of the glassy state.
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We investigate the quantum dynamics of Two-Level Systems (TLS) in glasses at low temperatures (1 K and below). We study an ensemble of TLSs coupled to phonons. By integrating out the phonons within the framework of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, we derive analytically the explicit form of the interactions among TLSs, and of the dissipation terms. We find that the unitary dynamics of the system shows clear signatures of Many-Body Localization physics. We study numerically the time behavior of the concurrence, which measures pairwise entanglement also in non-isolated systems, and show that it presents a power-law decay both in the absence and in the presence of dissipation, if the latter is not too large. These features can be ascribed to the strong, long-tailed disorder characterizing the distributions of the model parameters. Our findings show that assuming ergodicity when discussing TLS physics might not be justified for all kinds of experiments on low-temperature glasses.
Dynamical properties of vulcanized polymer networks are addressed via a Rouse-type model that incorporates the effect of permanent random crosslinks. The incoherent intermediate scattering function is computed in the sol and gel phases, and at the vulcanization transition between them. At any nonzero crosslink density within the sol phase Kohlrausch relaxation is found. The critical point is signalled by divergence of the longest time-scale, and at this point the scattering function decays algebraically, whereas within the gel phase it acquires a time-persistent part identified with the gel fraction.
We consider a class of random block matrix models in $d$ dimensions, $d ge 1$, motivated by the study of the vibrational density of states (DOS) of soft spheres near the isostatic point. The contact networks of average degree $Z = z_0 + zeta$ are represented by random $z_0$-regular graphs (only the circle graph in $d=1$ with $z_0=2$) to which Erdos-Renyi graphs having a small average degree $zeta$ are superimposed. In the case $d=1$, for $zeta$ small the shifted Kesten-McKay DOS with parameter $Z$ is a mean-field solution for the DOS. Numerical simulations in the $z_0=2$ model, which is the $k=1$ Newman-Watts small-world model, and in the $z_0=3$ model lead us to conjecture that for $zeta to 0$ the cumulative function of the DOS converges uniformly to that of the shifted Kesten-McKay DOS, in an interval $[0, omega_0]$, with $omega_0 < sqrt{z_0-1} + 1$. For $2 le d le 4$, we introduce a cutoff parameter $K_d le 0.5$ modeling sphere repulsion. The case $K_d=0$ is the random elastic network case, with the DOS close to the Marchenko-Pastur DOS with parameter $t=frac{Z}{d}$. For $K_d$ large the DOS is close for small $omega$ to the shifted Kesten-McKay DOS with parameter $t=frac{Z}{d}$; in the isostatic case the DOS has around $omega=0$ the expected plateau. The boson peak frequency in $d=3$ with $K_3$ large is close to the one found in molecular dynamics simulations for $Z=7$ and $8$.
As a guideline for experimental tests of the ideal glass transition (Random Pinning Glass Transition, RPGT) that shall be induced in a system by randomly pinning particles, we performed first-principle computations within the Hypernetted chain approximation and numerical simulations of a Hard Sphere model of glass-former. We obtain confirmation of the expected enhancement of glassy behaviour under the procedure of random pinning, which consists in freezing a fraction $c$ of randomly chosen particles in the positions they have in an equilibrium configuration. We present the analytical phase diagram as a function of $c$ and of the packing fraction $phi$, showing a line of RPGT ending in a critical point. We also obtain first microscopic results on cooperative length-scales characterizing medium-range amorphous order in Hard Spere glasses and indirect quantitative information on a key thermodynamic quantity defined in proximity of ideal glass transitions, the amorphous surface tension. Finally, we present numerical results of pair correlation functions able to differentiate the liquid and the glass phases, as predicted by the analytic computations.
Eigenstates of fully many-body localized (FMBL) systems are described by quasilocal operators $tau_i^z$ (l-bits), which are conserved exactly under Hamiltonian time evolution. The algebra of the operators $tau_i^z$ and $tau_i^x$ associated with l-bits ($boldsymbol{tau}_i$) completely defines the eigenstates and the matrix elements of local operators between eigenstates at all energies. We develop a non-perturbative construction of the full set of l-bit algebras in the many-body localized phase for the canonical model of MBL. Our algorithm to construct the Pauli-algebra of l-bits combines exact diagonalization and a tensor network algorithm developed for efficient diagonalization of large FMBL Hamiltonians. The distribution of localization lengths of the l-bits is evaluated in the MBL phase and used to characterize the MBL-to-thermal transition.
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