Condensed Matter Theory

Abstract:

We construct an exact map between a tight-binding model on any bipartite lattice in the presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the nonequilibrium steady state and the leading decay modes describing the relaxation at late times are related to the η-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model.

Abstract:

We consider the nonequilibrium time evolution of a translationally invariant state under a Hamiltonian with a localized defect. We discern the situations where a light cone spreads out from the defect and separates the system into regions with macroscopically different properties. We identify the light cone and propose a procedure to obtain a (quasi)stationary state describing the late time dynamics of local observables. As an explicit example, we study the time evolution generated by the Hamiltonian of the transverse-field Ising chain with a local defect that cuts the interaction between two sites (a quench of the boundary conditions alongside a global quench). We solve the dynamics exactly and show that the late time properties can be obtained with the general method proposed.

Abstract:

It is well established that gene regulation can be achieved through activator and repressor proteins that bind to DNA and switch particular genes on or off, and that complex metabolic networks determine the levels of transcription of a given gene at a given time. Using three complementary computational techniques to study the sequence-dependence of DNA denaturation within DNA minicircles, we have observed that whenever the ends of the DNA are constrained, information can be transferred over long distances directly by the transmission of mechanical stress through the DNA itself, without any requirement for external signalling factors. Our models combine atomistic molecular dynamics (MD) with coarse-grained simulations and statistical mechanical calculations to span three distinct spatial resolutions and timescale regimes. While they give a consensus view of the non-locality of sequence-dependent denaturation in highly bent and supercoiled DNA loops, each also reveals a unique aspect of long-range informational transfer that occurs as a result of restraining the DNA within the closed loop of the minicircles.