arXiv subjects
Publications and source records attributed to S. Mallik.
Transport coefficients in a hadronic gas have been calculated earlier in the imaginary time formulation of thermal field theory. The steps involved are to relate the defining retarded correlation function to the corresponding time-ordered one and to evaluate the latter in the conventional perturbation expansion. Here we carry out both the steps in the real time formulation.
The origin of fluctuations in the average number of intermediate mass fragments seen in experiments in small projectile like fragments is discussed. We argue that these can be explained on the basis of a recently proposed model of projectile fragmentation.
In a recent paper [Phys. Rev. C 044612 (2011)] we proposed a model for calculating cross-sections of various reaction products which arise from disintegration of projectile like fragment resulting from heavy ion collisions at intermediate or higher energy. The model has three parts: (1) abrasion, (2) disintegration of the hot abraded projectile like fragment (PLF) into nucleons and primary composites using a model of equilibrium statistical mechanics and (3) possible evaporation of hot primary composites. It was assumed that the PLF resulting from abrasion has one temperature T. Data suggested that while just one value of T seemed adequate for most cross-sections calculations, it failed when dealing with very peripheral collisions. We have now introduced a variable T=T(b) where b is the impact parameter of the collision. We argue there are data which not only show that T must be a function of b but, in addition, also point to an approximate value of T for a given b. We propose a very simple formula: T(b)=D_0+D_1(A_s(b)/A_0) where A_s(b) is the mass of the abraded PLF and A_0 is the mass of the projectile; D_0 and D_1 are constants. Using this model we compute cross-sections for several collisions and compare with data.
For projectile fragmentation we work out details of a model whose origin can be traced back to the Bevalac era. The model positions itself between the phenomenological EPAX parametrization and microscopic transport models like "Heavy Ion Phase Space Exploration Model" (HIPSE) and antisymmetrised molecular dynamics(AMD). We apply the model to some recent data of projectile fragmentation of Ni on Ta and Be at beam energy 140 MeV/nucleon and some older data of Xe on Al at beam energy 790 MeV/nucleon. Reasonable values of cross-sections for various composites populated in the reactions are obtained.
We present a simple calculation of the nucleon self-energy in nuclear matter at finite temperature in a relativistic framework, using the real time thermal field theory. The imaginary parts of one-loop graphs are identified with discontinuities across the unitary and the Landau cuts. We find that in general both the cuts contribute significantly to the spectral function in the region of (virtual) nucleon mass usually considered, even though the unitary cut is ignored in the literature. Also our relativistic spectral function differs from the one in non-relativistic approximation, used in some earlier calculations.
We analyse the structure of one-loop self-energy graphs for the rho meson in real time formulation of finite temperature field theory. We find the discontinuities of these graphs across the unitary and the Landau cuts. These contributions are identified with different sources of medium modification discussed in the literature. We also calculate numerically the imaginary and the real parts of the self-energies and construct the spectral function of the rho meson, which are compared with an earlier determination. A significant contribution arises from the unitary cut of the pi-omega loop, that was ignored so far in the literature.
We consider the two-point function of nucleon current in nuclear matter and write a QCD sum rule to analyse the residue of the nucleon pole as a function of nuclear density. The nucleon self-energy needed for the sum rule is taken as input from calculations using phenomenological NN potential. Our result shows a decrease in the residue with increasing nuclear density, as is known to be the case with similar quantities.
We derive a form of spectral representations for all bosonic and fermionic propagators in the real-time formulation of field theory at finite temperature and chemical potential. Besides being simple and symmetrical between the bosonic and the fermionic types, these representations depend explicitly on analytic functions only. This last property allows a simple evaluation of loop integrals in the energy variables over propagators in this form, even in presence of chemical potentials, which is not possible over their conventional form.
We calculate the equation of state of nuclear matter based on the general analysis of the grand canonical partition function in the $S$-matrix framework. In addition to the low mass stable particles and their two-body scattering channels considered earlier, the calculation includes systematically all the higher mass particles and their exited states as well as the scattering channels formed by any number of these species. We estimate the latter contribution by resonances in all the channels. The resulting model-independent virial series for pressure gets substantial contribution from the heavy particles and the channels containing them. The series converges for larger values of baryon density than found earlier.
We treat the propagation of nucleon in nuclear matter by evaluating the ensemble average of the two-point function of nucleon currents in the framework of the chiral effective field theory. We first derive the effective parameters of nucleon to one loop. The resulting formula for the effective mass was known previously and gives an absurd value at normal nuclear density. We then modify it following Weinberg's method for the two-nucleon system in the effective theory. Our results for the effective mass and the width of nucleon are compared with those in the literature.
We describe how the thermal counterpart of a vacuum two-point function may be obtained in the real time formalism in a simple way by using directly the $2\times 2$ matrices that different elements acquire in this formalism. Using this procedure we calculate the analytic (single component) thermal amplitude for the pion pole term in the ensemble average of two axial-vector currents to two loops in chiral perturbation theory. The general expressions obtained for the effective mass and decay constants of the pion are evaluated in the chiral and the nonrelativistic limits. We also investigate the effect of massive states on these effective parameters.
The vector and the axial-vector meson couplings with the vector and the axial-vector currents respectively at finite temperature have been obtained in Ref. \cite{Mallik} by calculating all the relevant one-loop Feynman graphs with vertices obtained from the effective chiral Lagrangian. On the other hand, the same couplings were also derived in Ref.\cite{Ioffe1} by applying the method of current algebra and the hypothesis of partial conservation of axial-vector current (PCAC). The latter method appears to miss certain terms; in the case of the vector meson coupling with the vector current, for example, a term containing the $ρωπ$ coupling is missed. A similar situation would also appear for the nucleon coupling with the nucleon current. In this note we resolve these differences.
In a box of size $L$, a spatially antisymmetric square-well potential of a purely imaginary strength ${\rm i}g$ and size $l < L$ is interpreted as an initial element of the SUSY hierarchy of solvable Hamiltonians, the energies of which are all real for $g < g_c(l)$. The first partner potential is constructed in closed form and discussed.
The simplest purely imaginary and piecewise constant $\cal PT$-symmetric potential located inside a larger box is studied. Unless its strength exceeds a certain critical value, all the spectrum of its bound states remains real and discrete. We interpret such a model as an initial element of the generalized non-Hermitian Witten's hierarchy of solvable Hamiltonians and construct its first supersymmetric (SUSY) partner in closed form.
We derive QCD sum rules from the nucleon two-point function in nuclear medium, calculating its specral function in chiral perturbation theory to one loop. Our calculation shows the inadequacy of the commonly used ansatz to represent the two-point function as the sum of a nucleon pole term and a spectral integral over the high energy continuum. We also point out that it is the energy variable and not its square that must be used in writing the dispersion integrals. The sum rules are obtained by equating terms linear in nucleon number density of the spectral and operator representations of the correlation function. We use them to predict the curent-nucleon coupling, in good agreement with the value known from the vacuum sum rules. They also predict a definite deviation of the four-quark condensate from its ground state saturation value.
We consider the nucleon self-energy in nuclear matter in the absence of Pauli blocking. It is evaluated using the partial-wave analysis of $NN$ scattering data. Our results are compared with that of a realistic calculation to estimate the effect of this blocking. It is also possible to use our results as a check on the realistic calculations.
We consider two methods to find the effective parameters of the pion traversing a nuclear medium. One is the first order chiral perturbation theoretic evaluation of the pion pole contribution to the two-point function of the axial-vector current. The other is the exact, first order virial expansion of the pion self-energy. We find that, although the results of chiral perturbation theory are not valid at normal nuclear density, those from the virial expansion may be reliable at such density. The latter predicts both the mass-shift and the in-medium decay width of the pion to be small, of about a few MeV.
We examine the classical problem of an infinite square well by considering Hamilton's equations in one dimension and Hamilton-Jacobi equation for motion in two dimensions. We illustrate, by means of suitable examples, the nature of the periodic motion of a particle trapped inside the well.