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Saibal Mitra

Publications and source records attributed to Saibal Mitra.

12 recordsLinked to original sources

Percolation clusters of organics in interstellar ice grains as the incubators of life

Biomolecules can be synthesized in interstellar ice grains subject to UV radiation and cosmic rays. I show that on time scales of $\gtrsim 10^{6}$ years, these processes lead to the formation of large percolation clusters of organic molecules. Some of these clusters would have ended up on proto-planets where large, loosely bound aggregates of clusters (superclusters) would have formed. The interior regions of such superclusters provided for chemical micro-environments that are filtered versions of the outside environment. I argue that models for abiogenesis are more likely to work when considered inside such micro-environments. As the supercluster breaks up, biochemical systems in such micro-environments gradually become subject to a less filtered environment, allowing them to get adapted to the more complex outside environment. A particular system originating from a particular location on some supercluster would have been the first to get adapted to the raw outside environment and survive there, thereby becoming the first microbe. A collision of a microbe-containing proto-planet with the Moon could have led to fragments veering off back into space, microbes in small fragments would have been able to survive a subsequent impact with the Earth.

astro-ph.EP

Changing the past by forgetting

Assuming the validity of the Many Worlds Interpretation (MWI) of quantum mechanics, we show that memory erasure can cause one to end up in a different sector of the multiverse where the contents of the erased memory is different.

quant-ph

Entangled states considered as physical representations of classical algorithms

There are good reasons to believe that we are classical algorithms run on (effectively) classical machines. However, the fact that a physical state of a system in a universe described by a classical deterministic model doesn't contain any information about the model's evolution laws, gives rise to deep philosophical paradoxes with this picture of what we are. We explain these paradoxes in detail and show that they can be resolved once we take into account that in the real world, classical behavior arises as a result of decoherence. We then show that this solution naturally leads to a variant of the idea of a mathematical multiverse, originally proposed by Tegmark.

quant-ph

Exact asymptotics of the characteristic polynomial of the symmetric Pascal matrix

We have obtained the exact asymptotics of the determinant $\det_{1\leq r,s\leq L}[\binom{r+s-2}{r-1}+\exp(iθ)δ_{r,s}]$. Inverse symbolic computing methods were used to obtain exact analytical expressions for all terms up to relative order $L^{-14}$ to the leading term. This determinant is known to give weighted enumerations of cyclically symmetric plane partitions, weighted enumerations of certain families of vicious walkers and it has been conjectured to be proportional to the one point function of the O$(1)$ loop model on a cylinder of circumference $L$. We apply our result to the loop model and give exact expressions for the asymptotics of the average of the number of loops surrounding a point and the fluctuation in this number. For the related bond percolation model, we give exact expressions for the asymptotics of the probability that a point is on a cluster that wraps around a cylinder of even circumference and the probability that a point is on a cluster spanning a cylinder of odd circumference.

math-ph

Detecting dark matter in electromagnetic field penetration experiments

Dark matter in the form of particles from a hidden mirror sector has recently been proposed as an explanation for the DAMA annual modulation signal. Here one assumes that there exists a small mixing between photons and mirror photons. We show that dark matter with this property can also be detected in electromagnetic field penetration experiments. Such experiments can be used to measure the speed and direction of the dark matter halo wind, the local density, the temperature, and the strength of the photon-mirror photon mixing interaction. An additional result would be a significant improvement of the upper limit on the photon mass.

astro-ph

Has DAMA Detected Self-Interacting Dark Matter?

We consider a model in which dark matter consists of a large self-interacting component (SIDM particles) and a small component with strong interactions with baryons (SIMPs). We show that the DAMA annual modulation signal can be caused by SIDM particles interacting with SIMPs trapped in iodine nuclei in the DAMA/NaI detector.

astro-ph

Uranus's anomalously low excess heat constrains strongly interacting dark matter

Dark matter annihilations can generate significant amounts of internal heat inside planets if dark matter consists mainly of particles with nuclear cross sections in the micro-barn range or larger (SIMPs). By considering a detailed model of Uranus's interior, we calculate upper limits on the S-wave annihilation cross section for these particles as a function of their mass. These upper limits, together with other experimental and theoretical constraints, rule out SIMPs with masses between 150 MeV and $10^{4}$ GeV.

astro-ph

Exact conjectured expressions for correlations in the dense O$(1)$ loop model on cylinders

We present conjectured exact expressions for two types of correlations in the dense O$(n=1)$ loop model on $L\times \infty$ square lattices with periodic boundary conditions. These are the probability that a point is surrounded by $m$ loops and the probability that $k$ consecutive points on a row are on the same or on different loops. The dense O$(n=1)$ loop model is equivalent to the bond percolation model at the critical point. The former probability can be interpreted in terms of the bond percolation problem as giving the probability that a vertex is on a cluster that is surrounded by $\floor{m/2}$ clusters and $\floor{(m+1)/2}$ dual clusters. The conjectured expression for this probability involves a binomial determinant that is known to give weighted enumerations of cyclically symmetric plane partitions and also of certain types of families of nonintersecting lattice paths. By applying Coulomb gas methods to the dense O$(n=1)$ loop model, we obtain new conjectures for the asymptotics of this binomial determinant.

cond-mat.stat-mech

Osculating Random Walks on Cylinders

We consider random paths on a square lattice which take a left or a right turn at every vertex. The possible turns are taken with equal probability, except at a vertex which has been visited before. In such case the vertex is left via the unused edge. When the initial edge is reached the path is considered completed. We also consider families of such paths which together cover every edge of the lattice once and visit every vertex twice. Because these paths may touch but not intersect each other and themselves, we call them osculating walks. The ensemble of such families is also known as the dense O$(n=1)$ model. We consider in particular such paths in a cylindrical geometry, with the cylindrical axis parallel with one of the lattice directions. We formulate a conjecture for the probability that a face of the lattice is surrounded by $m$ distinct osculating paths. For even system sizes we give a conjecture for the probability that a path winds round the cylinder. For odd system sizes we conjecture the probability that a point is visited by a path spanning the infinite length of the cylinder. Finally we conjecture an expression for the asymptotics of a binomial determinant.

math-ph

Expansions about Free-Fermion Models

A simple technique for expanding the free energy of general six-vertex models about free-fermion points is introduced. This technique is used to verify a Coulomb gas prediction about the behavior of the leading singularity in the free energy of the staggered F-model at zero staggered field.

math-ph

The XXZ spin chain at $Δ=- {1/2}$: Bethe roots, symmetric functions and determinants

A number of conjectures have been given recently concerning the connection between the antiferromagnetic XXZ spin chain at $Δ= - \frac12$ and various symmetry classes of alternating sign matrices. Here we use the integrability of the XXZ chain to gain further insight into these developments. In doing so we obtain a number of new results using Baxter's $Q$ function for the XXZ chain for periodic, twisted and open boundary conditions. These include expressions for the elementary symmetric functions evaluated at the groundstate solution of the Bethe roots. In this approach Schur functions play a central role and enable us to derive determinant expressions which appear in certain natural double products over the Bethe roots. When evaluated these give rise to the numbers counting different symmetry classes of alternating sign matrices.

math-ph

Renormalization Group Studies of Vertex Models

In this thesis we use renormalization group methods to study the critical behaviour of the staggered F-model. This model is a six vertex model that can be used to calculate the thermodynamic properties of a facet of a BCC crystal in the (100) direction.

physics.class-ph