Papers by Somendra Bhattacharjee
Journal of Physics Condensed Matter, Apr 12, 2006
We discuss the thermodynamic behaviour near the force induced unzipping transition of double-stra... more We discuss the thermodynamic behaviour near the force induced unzipping transition of double-stranded DNA in two different ensembles. The Y-fork is identified as the coexisting phases in the fixed distance ensemble. From finite size scaling of thermodynamic quantities like the extensibility and the length of the unzipped segment of a Y-fork, the phase diagram can be recovered. We suggest that such procedures could be used to obtain the thermodynamic phase diagram from experiments on finite length DNA.
Randomness in vertex models and directed walks
Journal of Physics a Mathematical General, Jul 1, 1992
The authors consider a d-dimensional random five vertex (modified KDP) model where the vertex ene... more The authors consider a d-dimensional random five vertex (modified KDP) model where the vertex energies are site dependent, uncorrelated random numbers (> 0). This model maps onto many directed walks in a random environment. They show that the upper critical ...
We study the bipartite von Neumann entropy of two particles interacting via a long-range scale-fr... more We study the bipartite von Neumann entropy of two particles interacting via a long-range scale-free potential $V(r)\sim -g/r^2$ in three dimensions, close to the unbinding transition. The nature of the quantum phase transition changes from critical ($-3/4<g<1/4$) to first order ($g<-3/4$) with $g=-3/4$ as a multicritical point. Here we show that the entanglement entropy has different behaviours for the critical and the first order regimes. But still there exists an interesting multicritical scaling behaviour for all $g\in (-2<g<1/4)$ controlled by the $g=-3/4$ case.
Exact matrix representation of the RVB wavefunction
Zeitschrift Fur Physik B Condensed Matter, Sep 30, 1991
ABSTRACT
Adsorption of fluid vesicles
The Journal of Chemical Physics, Sep 15, 1997
The adhesion of fluid vesicles to a planar surface has been studied using Monte Carlo methods and... more The adhesion of fluid vesicles to a planar surface has been studied using Monte Carlo methods and scaling arguments for the random surface model. Deflated as well as inflated vesicles have been considered. Inflated vesicles, with internal pressure p>0, exhibit with increasing adhesion strength a discontinuous conformational transition from unbound sphere-like conformations to strongly adsorbed two dimensional branched conformations. Deflated vesicles with p=0 exhibit a continuous transition from three dimensional to two dimensional branched conformations where the type of transition is different from adsorption transition of branched polymers. The transition temperatures scale according to ɛc/kT˜p√N, where N is the surface area of the vesicle.
LETTER TO THE EDITOR: Unzipping DNAs: towards the first step of replication
J Phys a Math Gen, 2000
It is shown that a double-stranded DNA can be opened by a force only if the force exceeds a criti... more It is shown that a double-stranded DNA can be opened by a force only if the force exceeds a critical value, and this unzipping is a critical phenomenon. From the results of an equivalent delocalization in a non-hermitian quantum mechanics problem we show the different scaling behaviours of unzipping by force and thermal melting. Based on this we make a postulate on the first step of replication of DNA.
The opening of the Y-fork - the first step of DNA replication - is shown to be a critical phenome... more The opening of the Y-fork - the first step of DNA replication - is shown to be a critical phenomenon under an external force at one of its ends. From the results of an equivalent delocalization in a non-hermitian quantum-mechanics problem we show the different scaling behavior of unzipping and melting. The resultant long-range critical features within the unzipped part of Y might play a role in the highly correlated biochemical functions during replication.
Journal of Physics a Mathematical and Theoretical, 2007
The idea of duality in one-dimensional nonequilibrium transport is introduced by generalizing the... more The idea of duality in one-dimensional nonequilibrium transport is introduced by generalizing the observations by Mukherji and Mishra. A general approach is developed for the classification and characterization of the steady state phase diagrams which are shown to be determined by the nature of the zeros of a set of coarse-grained functions that encode the microscopic dynamics. A new class of nonequilibrium multicritical points has been identified.
The effects of two types of randomness on the behaviour of directed polymers are discussed in thi... more The effects of two types of randomness on the behaviour of directed polymers are discussed in this chapter. The first part deals with the effect of randomness in medium so that a directed polymer feels a random external potential. The second part deals with the RANI model of two directed polymers with heterogeneity along the chain such that the interaction is random. The random medium problem is better understood compared to the RANI model.
Physical Review B Condensed Matter, Mar 1, 1996
We consider the behavior of the overlap of $m (\geq 2)$ paths at the spin glass transition for a ... more We consider the behavior of the overlap of $m (\geq 2)$ paths at the spin glass transition for a directed polymer in a random medium. We show that an infinite number of exponents is required to describe these overlaps. This is done in an $\epsilon = d-2$ expansion without using the replica trick.
Physical Review E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics, Jan 10, 2001
We use a renormalization group to calculate the reunion and survival exponents of a set of random... more We use a renormalization group to calculate the reunion and survival exponents of a set of random walkers interacting with a long range 1/r2 and a short range interaction. These exponents are used to study the binding-unbinding transition of polymers and the behavior of several quantum problems.
Current Science, Nov 1, 1995
The exact solution of the two-dimensional Ising model by Onsager in 1944 represents one of the la... more The exact solution of the two-dimensional Ising model by Onsager in 1944 represents one of the landmarks in theoretical physics. On the occassion of the fifty years of the exact solution, we give a historical review of this model. After briefly discussing the exact solution by Onsager, we point out some of the recent developments in this field. The exact solution by Onsager has inspired several developments in various other fields. Some of these are also briefly mentioned.
A three-stranded DNA with short range base pairings only is known to exhibit a classical analog o... more A three-stranded DNA with short range base pairings only is known to exhibit a classical analog of the quantum Efimov effect, viz., a three chain bound state at the two chain melting point where no two are bound. By using a non-perturbative renormalization group method for a rigid duplex DNA and a flexible third strand, with base pairings and strand exchange, we show that the Efimov-DNA is associated with a limit cycle type behavior of the flow of an effective three chain interaction. The analysis also shows that thermally generated bubbles play an essential role in producing the effect. A toy model for the flow equations shows the limit cycle in an extended three dimensional parameter space of the two-chain coupling and a complex three chain interaction.
Our aim in this set of lectures is to give an introduction to critical phenomena that emphasizes ... more Our aim in this set of lectures is to give an introduction to critical phenomena that emphasizes the emergence of and the role played by diverging length-scales. It is now accepted that renormalization group gives the basic understanding of these phenomena and so, instead of following the traditional historical trail, we try to develop the subject in a way that emphasizes the length-scale based approach.
Thermal denaturation of DNA is often studied with coarse-grained models in which native sequentia... more Thermal denaturation of DNA is often studied with coarse-grained models in which native sequential base pairing is mimicked by the existence of attractive interactions only between monomers at the same position along strands (Poland and Scheraga models). Within this framework, the existence of a three strand DNA bound state in conditions where a duplex DNA would be in the denaturated state was recently predicted from a study of three directed polymer models on simplified hierarchical lattices ($d>2$) and in $1+1$ dimensions. Such phenomenon which is similar to the Efimov effect in nuclear physics was named Efimov-DNA. In this paper we study the melting of the three-stranded DNA on a Sierpinski gasket of dimensions $d<2$ by assigning extra weight factors to fork openings and closings, to induce a two-strand DNA melting. In such a context we can find again the existence of the Efimov-DNA-like state but quite surprisingly we discover also the presence of a different phase, to be called a mixed state, where the strands are pair-wise bound but without three chain contacts. Whereas the Efimov DNA turns out to be a crossover near melting, the mixed phase is a thermodynamic phase.
Indian Journal of Physics a and Proceedings of the Indian Association For the Cultivation of Science a, 2002
Statistical Mechanics of Anisotropic Dimer Models
ABSTRACT
The exact solution of the two-dimensional Ising model by Onsager in 1944 represents one of the la... more The exact solution of the two-dimensional Ising model by Onsager in 1944 represents one of the landmarks in theoretical physics. On the occassion of the fifty years of the exact solution, we give a historical review of this model.
This is a set of introductory lectures on the behaviour of a directed polymer in a random medium.... more This is a set of introductory lectures on the behaviour of a directed polymer in a random medium. Both the intuitive picture that helps in developing an understanding and systematic approaches for quantitative studies are discussed.
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we s... more A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are pointed out, by paraphrasing the laws of thermodynamics for computers. Also discussed is an approach that may be adopted to develop statistical mechanics using the algorithmic point of view.
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Papers by Somendra Bhattacharjee