Dynamical phase transition of a periodically driven DNA

Replication and transcription are two important processes in living systems. To execute such processes, various proteins work far away from equilibrium in a staggered way. Motivated by this, aspects of hysteresis during unzipping of DNA under a periodic drive in non-equilibrium conditions are studied. A steady state phase diagram of a driven DNA is proposed which is experimentally verifiable. As a two state system, we also compare the results of DNA with that of an Ising magnet under an asymmetrical variation of magnetic field.Comment: 8 pages, 6 figures, Accepted version in PR

Entanglement entropy of a quantum unbinding transition and entropy of DNA

Two significant consequences of quantum fluctuations are entanglement and criticality. Entangled states may not be critical but a critical state shows signatures of universality in entanglement. A surprising result found here is that the entanglement entropy may become arbitrarily large and negative near the dissociation of a bound pair of quantum particles. Although apparently counter-intuitive, it is shown to be consistent and essential for the phase transition, by mapping to a classical problem of DNA melting. We associate the entanglement entropy to a subextensive part of the entropy of DNA bubbles, which is responsible for melting. The absence of any extensivity requirement in time makes this negative entropy an inevitable consequence of quantum mechanics in continuum. Our results encompass quantum critical points and first-order transitions in general dimensions.Comment: v2: 6 pages, 3 figures (title modified, more details and figures added

TYPE II DNA: when the interfacial energy becomes negative

An important step in transcription of a DNA base sequence to a protein is the initiation from the exact starting point, called promoter region. We propose a physical mechanism for identification of the promoter region, which relies on a new classification of DNAs into two types, Type-I and Type-II, like superconductors, depending on the sign of the energy of the interface separating the zipped and the unzipped phases. This is determined by the energies of helical ordering and stretching over two independent length scales. The negative interfacial energy in Type II DNA leads to domains of helically ordered state separated by defect regions, or blobs, enclosed by the interfaces. The defect blobs, pinned by non-coding promoter regions, would be physically distinct from all other types of bubbles. We also show that the order of the melting transition under a force is different for Type I and Type II.Comment: 4 pages, 2 figures, Eq.(4) corrected in 4th versio

Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions

Driving a homogeneous system across a quantum phase transition in a quench-time $\tau_Q$ generates excitations on wavelengths longer than the Kibble-Zurek (KZ) length $\hat\xi\propto\tau_Q^{\nu/(1+z\nu)}$ within the KZ time window $\hat t\propto\tau_Q^{z\nu/(1+z\nu)}$, where $z$ and $\nu$ are the critical exponents. Quenches designed with local time-dependent inhomogeneity can introduce a gap in the spectrum. For a variety of setups with short-range interactions, they have been shown to suppress excitations if the spatial velocity of the inhomogenous front is below the characteristic KZ velocity $\hat v \propto \hat\xi/\hat t$. Ising-like models with long-range interactions can have no sonic horizon, spreading information instantaneously across the system. Usually, this should imply that inhomogenous transitions will render the dynamics adiabatic regardless of the front velocity. However, we show that we get an adiabatic transition with no defects only when the inhomogeneous front moves slower than a characteristic crossover velocity $\tilde v \propto \theta^{(z-1)\nu/(1+\nu)}$, where $\theta$ is the slope of the inhomogeneous front at the critical point. The existence of this crossover velocity and adiabaticity of the model is a consequence of the energy gap in the quasiparticle spectrum that is opened by the inhomogeneity. This effect can be employed for efficient adiabatic quantum state preparation in systems with long-range interactions.Comment: 12 pages, 10 figures (closed to published version

An integrated and open-ended experiment: study of chemical waves in time and space

In this article we discuss an exciting experiment in non-linear dynamics. This provides an imaginative platform for bringing in chemical, physical, biological, mathematical and computational sciences together. There are implications for earth sciences as well