arXiv subjects

M. V. N. Murthy

Publications and source records attributed to M. V. N. Murthy.

At least 37 records · Page 2Linked to original sources

arXiv2009

Cold atoms at unitarity and inverse square interaction

Consider two identical atoms in a spherical harmonic oscillator interacting with a zero-range interaction which is tuned to produce an s-wave zero-energy bound state. The quantum spectrum of the system is known to be exactly solvable. We note that the same partial wave quantum spectrum is obtained by the one-dimensional scale-invariant inverse square potential. Long known as the Calogero-Sutherland-Moser (CSM) model, it leads to Fractional Exclusion Statistics (FES) of Haldane and Wu. The statistical parameter is deduced from the analytically calculated second virial coefficient. When FES is applied to a Fermi gas at unitarity, it gives good agreement with experimental data without the use of any free parameter.

cond-mat.quant-gas↗

arXiv2009

The virial expansion of a classical interacting system

We consider N particles interacting pair-wise by an inverse square potential in one dimension (Calogero-Sutherland-Moser model). When trapped harmonically, its classical canonical partition function for the repulsive regime is known in the literature. We start by presenting a concise re-derivation of this result. The equation of state is then calculated both for the trapped and the homogeneous gas. Finally, the classical limit of Wu's distribution function for fractional exclusion statistics is obtained and we re-derive the classical virial expansion of the homogeneous gas using this distribution function.

cond-mat.stat-mech↗

arXiv2008

Fermionic ground state at unitarity and Haldane Exclusion Statistics

We consider a few-particle system of trapped neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate the energies and the spatial densities of the few-body systems using a generalisation of the extended Thomas-Fermi (ETF) method, and assuming the particles obey the Haldane-Wu fractional exclusion statistics (FES) at unitarity. This method is different from the scaled ETF version given by Chang and Bertsch (Phys. Rev. A76,021603(R) (2007)). Our semiclassical FES results are consistent with the Monte-Carlo calculations of the above authors, but can hardly be distinguished from their over all scaling of the ETF result at unitarity.

cond-mat.other↗

arXiv2007

Coupling of Surface and Volume Dipole Oscillations in C-60 Molecules

We first give a short review of the ``local-current approximation'' (LCA), derived from a general variation principle, which serves as a semiclassical description of strongly collective excitations in finite fermion systems starting from their quantum-mechanical mean-field ground state. We illustrate it for the example of coupled translational and compressional dipole excitations in metal clusters. We then discuss collective electronic dipole excitations in C$_{60}$ molecules (Buckminster fullerenes). We show that the coupling of the pure translational mode (``surface plasmon'') with compressional volume modes in the semiclasscial LCA yields semi-quantitative agreement with microscopic time-dependent density functional (TDLDA) calculations, while both theories yield qualitative agreement with the recent experimental observation of a ``volume plasmon''.

physics.atm-clus↗

arXiv2006

Fermions at unitarity and Haldane Exclusion Statistics

We consider a gas of neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate, the variation of the chemical potential and the energy per particle as a function of temperature by assuming the system to be an ideal gas obeying the Haldane-Wu fractional exclusion statistics. Our results for the untrapped gas compare favourably with the recently published Monte Carlo calculations of two groups. For a harmonically trapped gas, the results agree with experiment, and also with other published work.

cond-mat.other↗

arXiv2006

Neutrino oscillation probabilities: Sensitivity to parameters

We study in detail the sensitivity of neutrino oscillation probabilities to the fundamental neutrino parameters and their possible determination through experiments. The first part of the paper is devoted to the broad theme of isolating regions in the neutrino (and anti-neutrino) energy and propagation length that are sensitive to the oscillation parameters. Such a study is relevant to neutrinos both from the Earth's atmosphere or from a neutrino factory. For completeness we discuss the sensitivity, however small, to the parameters involved in a three-generation framework, and to the Earth matter density profile. We then study processes relevant to atmospheric neutrinos which are sensitive to and allow precision measurements of the mixing angle theta_23 and mass-squared difference delta_32 apart from the mixing angle theta_13. Crucial to this analysis is charge identification; detectors having this capability can isolate these matter effects. In particular, we address the issue of using matter effects to determine whether the mixing angle theta_23 is maximal, and, if not, to explore how well its octant can be determined. When realistic detector resolutions are included, we find that deviations of about 15% (20%) from a maximal value of sin^2 theta_23=1/2 can be measured at 95% (99%) CL provided theta_13 is non-zero, sin^2 theta_13 >= 0.015, and the neutrino mass ordering is normal, with fairly large exposures of 1000 kton-years.

hep-ph↗

arXiv2005

Gentile statistics and restricted partitions

In a recent paper (Tran et al., Ann.Phys.311(2004)204), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We generalise these results to obtain an asymptotic formula for the restricted or coloured partitions p_k^s(n), which is the number of partitions of an integer n into the summand of s^{th} powers of integers such that each power of a given integer may occur utmost k times. While the method is not rigorous, it reproduces the well known asymptotic results for s=1 apart from yielding more general results for arbitrary values of s.

math-ph↗

arXiv2004

A question of hierarchy: matter effects with atmospheric neutrinos and anti-neutrinos

It is by now established that neutrinos mix, have (different) non-zero masses, and therefore oscillate. The oscillation parameters themselves, however, are not all well-known. An open problem is that of the neutrino mass hierarchy. We study the possibility of determining the neutrino mass hierarchy with atmospheric neutrinos using an iron calorimeter detector capable of charge identification such as the proposed MONOLITH and ICAL/INO detectors. We find that such detectors are sensitive to the sign of the mass-squared difference, δ_{32} = m_3^2 - m_2^2, provided the as-yet unknown mixing angle between the first and third generations, θ_{13}, is greater than 6 degrees (\sin^2 2θ_{13} > 0.04). A result with a significance greater than 90% CL requires large exposures (more than 500 kton-years) as well as good energy and angular resolution of the detected muons (better than 15%), especially for small θ_{13}. Hence obtaining definitive results with such a detector is difficult, unless θ_{13} turns out to be large. In contrast, such detectors can establish a clear oscillation pattern in atmospheric neutrinos in about 150 kton-years, therefore determining the absolute value of δ_{32} and \sin^2 2 θ_{23} to within 10%.

hep-ph↗

arXiv2003

On the Quantum Density of States and Partitioning an Integer

This paper exploits the connection between the quantum many-particle density of states and the partitioning of an integer in number theory. For $N$ bosons in a one dimensional harmonic oscillator potential, it is well known that the asymptotic (N -> infinity) density of states is identical to the Hardy-Ramanujan formula for the partitions p(n), of a number n into a sum of integers. We show that the same statistical mechanics technique for the density of states of bosons in a power-law spectrum yields the partitioning formula for p^s(n), the latter being the number of partitions of n into a sum of s-th powers of a set of integers. By making an appropriate modification of the statistical technique, we are also able to obtain d^s(n) for distinct partitions. We find that the distinct square partitions d^2(n) show pronounced oscillations as a function of n about the smooth curve derived by us. The origin of these oscillations from the quantum point of view is discussed. After deriving the Erdos-Lehner formula for restricted partitions for the $s=1$ case by our method, we generalize it to obtain a new formula for distinct restricted partitions.

math-ph↗

arXiv2003

Classical and Quantum Mechanics of Anyons

We review aspects of classical and quantum mechanics of many anyons confined in an oscillator potential. The quantum mechanics of many anyons is complicated due to the occurrence of multivalued wavefunctions. Nevertheless there exists, for arbitrary number of anyons, a subset of exact solutions which may be interpreted as the breathing modes or equivalently collective modes of the full system. Choosing the three-anyon system as an example, we also discuss the anatomy of the so called ``missing'' states which are in fact known numerically and are set apart from the known exact states by their nonlinear dependence on the statistical parameter in the spectrum. Though classically the equations of motion remains unchanged in the presence of the statistical interaction, the system is non-integrable because the configuration space is now multiply connected. In fact we show that even though the number of constants of motion is the same as the number of degrees of freedom the system is in general not integrable via action-angle variables. This is probably the first known example of a many body pseudo-integrable system. We discuss the classification of the orbits and the symmetry reduction due to the interaction. We also sketch the application of periodic orbit theory (POT) to many anyon systems and show the presence of eigenvalues that are potentially non-linear as a function of the statistical parameter. Finally we perform the semiclassical analysis of the ground state by minimizing the Hamiltonian with fixed angular momentum and further minimization over the quantized values of the angular momentum.

cond-mat↗

arXiv2002

Harmonically trapped fermion gases: exact and asymptotic results in arbitrary dimensions

We investigate the particle and kinetic energy densities of harmonically trapped fermion gases at zero temperature in arbitrary dimensions. We derive analytically a differential equation connecting these densities, which so far have been proven only in one or two dimensions, and give other interesting relations involving several densities or the particle density alone. We show that in the asymptotic limit of large particle numbers, the densities go over into the semi-classical Thomas-Fermi (TF) densities. Hereby the Fermi energy to be used in the TF densities is identified uniquely. We derive an analytical expansion for the remaining oscillating parts and obtain very simple closed forms for the leading-order oscillating densities. Finally, we show that the simple TF functional relation $τ_{TF}[ρ]$ between kinetic and particle density is fulfilled also for the asymptotic quantum densities $τ(r)$ and $ρ(r)$ including their leading-order oscillating terms.

cond-mat.mes-hall↗

arXiv2002

Number Fluctuation in an interacting trapped gas in one and two dimensions

It is well-known that the number fluctuation in the grand canonical ensemble, which is directly proportional to the compressibility, diverges for an ideal bose gas as T -> 0. We show that this divergence is removed when the atoms interact in one dimension through an inverse square two-body interaction. In two dimensions, similar results are obtained using a self-consistent Thomas-Fermi (TF) model for a repulsive zero-range interaction. Both models may be mapped on to a system of non-interacting particles obeying the Haldane-Wu exclusion statistics. We also calculate the number fluctuation from the ground state of the gas in these interacting models, and compare the grand canonical results with those obtained from the canonical ensemble.

cond-mat.stat-mech↗

arXiv2002

Implications of recent solar neutrino observations: an analysis of charged current data

We have analysed the recent results from the observation of charged current ν_e d \to e^- p p events from solar neutrinos by the Sudbury Neutrino Observatory SNO assuming neutrino oscillations with three active flavours. The data seem to prefer a low mass-squared difference and large mixing angle solution (the so-called LOW solution) in (12) parameter space. However, when combined with the Gallium charged current interaction data from Gallex and GNO, distinct (1σ) allowed regions corresponding to the large mixing angle (LMA) and small mixing angle (SMA) appear while the LOW solution is disfavoured upto 3σstandard deviation. The physical electron neutrino survival probability corresponding to these best fit solutions are then determined and analysed for their energy dependence.

hep-ph↗

arXiv2001

Discussion on a possible neutrino detector located in India

We have identified some important and worthwhile physics opportunitites with a possible neutrino detector located in India. Particular emphasis is placed on the geographical advantage with a stress on the complimentary aspects with respect to other neutrino detectors already in operation.

hep-ph↗

arXiv2001

Solitons in one-dimensional interacting Bose-Einstein system

A modified Gross-Pitaevskii approximation was introduced recently for bosons in dimension $d\le2$ by Kolomeisky {\it et al.} (Phys. Rev. Lett. {\bf 85} 1146 (2000)). We use the density functional approach with sixth-degree interaction energy term in the Bose field to reproduce the stationary-frame results of Kolomeisky {\it et al.} for a one-dimensional Bose-Einstein system with a repulsive interaction. We also find a soliton solution for an attractive interaction, which may be boosted to a finite velocity by a Galilean transformation. The stability of such a soliton is discussed analytically. We provide a general treatment of stationary solutions in one dimension which includes the above solutions as special cases. This treatment leads to a variety of stationary wave solutions for both attractive and repulsive interactions.

cond-mat.stat-mech↗

arXiv2001

Neutrinos from Stellar Collapse: Comparison of signatures in water and heavy water detectors

Signatures of neutrino and antineutrino signals from stellar collapse in heavy water detectors are contrasted with those in water detectors. The effects of mixing, especially due to the highly dense matter in the supernova core, are studied. The mixing parameters used are those sets allowed by current understanding of available neutrino data: from solar, atmospheric and laboratory neutrino experiments. Signals at a heavy water detector, especially the dominant charged current reactions on deuteron, are very sensitive to some of these sets of allowed mixing parameters. Theoretical uncertainties on supernova neutrino spectra notwithstanding, a combination of supernova measurements with water and heavy water detectors may be able to distinguish many of these mixing possibilities and thus help in ruling out many of them.

hep-ph↗

arXiv2001

Twocomponent Fermi vapour in a 2D rotating trap

An exactly solvable model of two-component interacting Fermi vapour in two dimension within Thomas Fermi approach has been proposed. We assume a realistic off-diagonal s-wave interaction between fermions in the two hyperfine states. The interaction is taken to be given by a screened Coulomb interaction which is both relevant and is analytically tractable. There are two distinct limits in the case of trapped fermionic systems: When the rotating frequency is less than the trap frequency a Thomas-Fermi approach may be used for a reasonably large number of particles. In the case of rapidly rotating fermions, an alternative variational approach is used, where the local density approximation may be applied after projecting the system on to the lowest degenerate level. Analytic expressions for the relevant physical quantities are obtained and their significance is discussed in both these cases.

cond-mat.mes-hall↗

arXiv2000

Rotating fermions in two dimensions: Thomas Fermi approach

Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy functional for a finite fermionic system within the Thomas-Fermi approximation in two dimensions. We show that for specific interactions the problem may be exactly solved. We derive analytical expressions for the density, the critical size as well as the ground state energy of such systems in a given angular momentum sector.

cond-mat.mes-hall↗