Active transport in the cytoplasm plays critical roles in living cell physiology. However, the mechanical resistance that intracellular compartments experience, which is governed by the cytoplasmic material property, remains elusive, especially its dependence on size and speed. Here we use optical tweezers to drag a bead in the cytoplasm and directly probe the mechanical resistance with varying size and speed We introduce a method, combining the direct measurement and a simple scaling analysis, to reveal different origins of the size- and speed-dependent resistance in living mammalian cytoplasm. We show that the cytoplasm exhibits size-independent viscoelasticity as long as the effective strain rate / is maintained in a relatively low range (0.1 s < / < 2 s) and exhibits size-dependent poroelasticity at a high effective strain rate regime (5 s < / < 80 s). Moreover, the cytoplasmic modulus is found to be positively correlated with only / in the viscoelastic regime but also increases with the bead size at a constant / in the poroelastic regime. Based on our measurements, we obtain a full-scale state diagram of the living mammalian cytoplasm, which shows that the cytoplasm changes from a viscous fluid to an elastic solid, as well as from compressible material to incompressible material, with increases in the values of two dimensionless parameters, respectively. This state diagram is useful to understand the underlying mechanical nature of the cytoplasm in a variety of cellular processes over a broad range of speed and size scales.

Renormalization is one of the basic notions of condensed matter physics. Based on the concept of renormalization, the Landau's Fermi liquid theory has been able to explain, why despite the presence of Coulomb interactions, the free electron theory works so well for simple metals with extended Fermi surface (FS). The recent synthesis of graphene has provided the condensed matter physicists with a low energy laboratory of Dirac fermions where instead of a FS, one has two Fermi points. Many exciting phenomena in graphene can be successfully interpreted in terms of free Dirac electrons. In this paper, employing dynamical mean field theory (DMFT), we show that an interacting Dirac sea is essentially an effective free Dirac theory. This observation suggests the notion of Dirac liquid as a fixed point of interacting 2+1 dimensional Dirac fermions. We find one more fixed point at strong interactions describing a Mott insulating state, and address the nature of semi-metal to insulator (SMIT) transition in this system.

We elucidate the reduction of the winding number (WN) caused by the onsite disorder in a higher WN next nearest neighbor XY model. When disorder becomes strong enough, Majorana edge modes become critically extended, beyond which they collapse into Anderson localized (AL) states in the bulk, resulting in a topological Anderson insulating state (TAI). We identify a resilience threshold Wt for every pair of Majorana fermions (MFs). In response to increasing disorder every pair of MFs collapse into AL bulk at their resilience threshold. For very strong disorder, all Majorana fermions collapse and a topologically trivial state is obtained. We show that the threshold values are deeply related to the localization length of Majorana fermions, which can be efficiently calculated by an appropriate modification of the transfer matrix method. At the topological transition point, localization length of the zero modes diverges and the system becomes scale invariant. The number of peaks in the localization length as the function of disorder strength determines the number of zero modes in the clean state before disorder is introduced. This finding elevates the transfer matrix method to the level of a tool for determination of the topological index of both clean and disordered systems.

Phase transitions in the Hubbard model and ionic Hubbard model at half-filling on the honeycomb lattice are investigated in the strong coupling perturbation theory which corresponds to an expansion in powers of the hopping t around the atomic limit. Within this formulation we find analytic expressions for the single-particle spectrum, whereby the calculation of the insulating gap is reduced to a simple root finding problem. This enables high precision determination of the insulating gap that does not require any extrapolation procedure. The critical value of Mott transition on the honeycomb lattice is obtained to be Uc ≈ 2.38t. Studying the ionic Hubbard model at the lowest order, we find two insulating states, one with Mott character at large U and another with single-particle gap character at large ionic potential, ∆. The present approach gives a critical gapless state at U = 2∆ at lowest order. By systematically improving on the perturbation expansion, the density of states around this critical gapless phase reduces.