Theoretical Studies

1. Density Functional Theory and Its Application

   The optical response properties play an important role in characterizing atoms, molecules and solids. Therefore, calculating these properties constitutes an important part of both experimental and theoretical studies of many-electron systems.  We have developed a variation-perturbation (VP) method both within the orbital based Kohn-Sham (KS) and the particle- and the current- density based hydrodynamic approaches within Density functional theory (DFT) and its time dependent variant TDDFT.
   
   We have also demonstrated the applicability of VP methods within TDDFT by calculating dynamic linear and nonlinear polarizabilities of atoms and alkali metal clusters. We emphasize here the hydrodynamic based method developed by us is specially suited for extended systems (like large clusters) for which orbital based approach is computationally demanding.  We demonstrated this by calculating dynamic polarizabilities, van der Waals coefficients and collective excitation frequencies of large alkali metal clusters and also studied evolution of these properties with the size of cluster.

   Few Related References:

   • "Perturbation theory in terms of electron density" M. K. Harbola and A. Banerjee, Phys. Lett. A 222, 315 (1996).
   • "Variation-perturbation method in time-dependent density-functional theory", A. Banerjee and M. K. Harbola, Phys.Lett. A 236, 525 (1997).
   • "Hydrodynamic approach to time-dependent density functional theory; response properties of metal clusters". A. Banerjee and M. K. Harbola , J. Chem. Phys. 113, 5614 (2000).
   • "Many-electron problem in terms of the density: from Thomas-Fermi to Modern density-functional". M. K. Harbola and A. Banerjee, J. Theo. Comp. Chem.. 2, 301 (2003).
   • Hydrodynamical approach to collective oscillations in metal clusters
     Arup Banerjee and  Manoj K. Harbola,
     Phys. Lett. A  372  2881 (2008).
     
     
2. Ab initio study of nanoclusters

   During last two decades rapid progress in the experimental methods of producing atomic and molecular clusters in controlled fashion along with the development of sophisticated theoretical tools to handle such finite-sized fermionic systems at the ab initio level led to emergence of the field of cluster science as one of the most exciting and productive disciplines of physics, chemistry, and material science. We have carried out DFT/TDDFT based ab inito study of various ground state and optical response properties of alkali-metal (Li, Na, K), semiconductor (GaAs and GaP), and noble-metal clusters (Au).  Our recent study on doped Au clusters (Au19X, where X = doped atom, Li, Na, K, Rb, Cs, Cu, and Ag) has shown that doped gold cluster with Li and Cu are more stable than parent Au20 cluster making negative ion of these doped clusters better nanocatalysts.
   
   We have also carried out calculation of co-efficient of van der Waals interaction (C6) between variety of nanoclusters, atoms, molecules, and nanotubes by employing TDDFT. To calculate C6 we make use of the relationship that exists between it and the frequency dependent polarizability. Using this formalism we have estimated interaction strength between carbon nanotube and several molecules like green house gases (CO, CO2) , ozone molecule, and H2 molecule.  We have found that above-mentioned molecules have very high value of C6 indicating that the carbon nanotube may act as a good adsorbent for these gases.

   Few Related References:

   • Time-dependent density functional theory calculation of van der Waals coefficient of sodium clusters
     Arup Banerjee, Aparna Chakrabarti, and Tapan K. Ghanty, 
     J. Chem. Phys. 127, 134103 (2007)
   • “Ab initio study of properties of small potassium clusters”.
     Arup Banerjee,  Tapan K. Ghanty, and , Aparna Chakrabarti
     J. Phys. Chem.  112, 12303 (2008).
   • “Estimation of van der Waals interaction between molecules and carbon nanostructures:
     A time dependent density functional theory study”
     C. Kamal, T. K. Ghanty, Arup Banerjee, and A. Chackraborti
     J. Chem.  Phys.  131,  164708 (2009).
   • Structures and electronic properties of Au19X clustes  ( X = Li, Na, K,  Rb, Cs, Cu, and Ag)”
     T. K. Ghanty, Arup Banerjee, and A. Chackrabarti
     J. Phys. Chem. C 114, 20  (2010).
     
     
3. Confined atoms and molecules

   Atoms and molecules under spatial confinement show substantially different ground state and response properties as compared to their free counterparts.  These confined systems are finding applications in several problems of physics and chemistry.  For example, atoms trapped in cavities, zeolite channel or encapsulated in hollow cages of carbon-based nano-materials. The study of confined atoms also provides insight into various properties of quantum nanostructures and also in the investigation of effect of high pressure on the physical and chemical properties of atoms, ions and molecules. We have carried out studies on the spectroscopic and optical response properties of confined hydrogen and helium atoms.  The energies of ground state and three low lying excited states of confined helium atom in an impenetrable spherical box have been calculated by employing two-parameter variational correlated wave function. We have also employed DFT to calculate the energies and linear and non-linear polarizabilities of confined helium atom.

   Few Related References:
   • "Mean excitation energy, static polarizability, and hyperpolarizability of the spherically confined hydrogen atom".
     Arup. Banerjee , K. D. Sen, J. Garza and R. Vargas,
     J. Chem. Phys. 116, 4054 (2002) .
   • “Calculation of ground- and excited-state energies of confined helium atom”.
     Arup Banerjee, C. Kamal and  A. Chowdhury ,
     Phys. Lett  A 350, 121 (2006).
     
     
4. Bose-Einstein Condensation in Atomic Gases

   Bose-Einstein condensation in atomic gases is an active field of research. Theoretically the condensate of atomic gases is well described by the Gross-Pitaevskii  (GP) equation. A variational method is developed to solve the GP equation. This method leads to accurate results for the properties of the condensates in comparison to the ab-initio results.  We have also focused our attention on the effect of going beyond mean field approximation on the static properties and the collective oscillation frequencies of trapped condensate.  The need to go beyond mean field arises when the density or the scattering length characterizing interaction between condensate atoms become large. Experimentally such conditions have been achieved recently.  We have theoretically studied the modification in the density profile of a trapped condensate and the change in the frequencies of quadrupole mode of collective oscillation due to beyond mean field effects in the boson-boson interaction. We have also studied the effect of going beyond mean field on the static and the dynamic properties of BEC with quantized vortex state.
   
   The successful achievement of condensation in cold atomic gases has also led to active research on the degenerate Fermi gases obtained through cold fermionic atoms and also the mixtures of bosonic and fermionic atoms. We have investigated the effect of unequal masses of Bose and Fermi atoms on the collective oscillations of the Bose-Fermi mixtures. We find that the nature of collective oscillation of the mixture critically depends on the ratio of boson-fermion masses.

   Few Related References:
   
   
   • " Ground state properties and vortex state of Bosons in anisotropic trap: A variational approach" M. P. Singh and A. L. Satheesha,
     Eur. Phys. J. D 7, 391 (1999).
   • "Ground-state properties of a trapped Bose gas beyond the mean-field approximation"
     Arup Banerjee and M. P. Singh ,
     Phys. Rev. A. 64, 063604 (2001).
   • "Elementary excitation of a trapped bose gas in the large gas parameter limit"
     Arup Banerjee and M. P. Singh ,
     Phys. Rev. A. 66, 043609 (2002).
   • Collective oscillations of a Bose-Fermi mixture: Effect of unequal masses of Bose and Fermi particles”
     Arup Banerjee, Phys. Rev. A 76, 023611 (2007).
   • .“Dipole oscillations of a Bose-Fermi mixture: Effect of  unequal masses of Bose and Fermi particles”
     Arup Banerjee
     J. Phys. B At. Mol. Opt. Phys. 42, 235301 (2009).
     
     
5. Neural Networks

   Studied two variants of a celebrated neural network model of associative memory, the Hopfield model: (i) a Hopfield model with random asymmetric interactions and (ii) a Hopfield model with self-coupling, and a one pattern model with random asymmetric couplings. It is shown that the introduction of the antisymmetric component in the otherwise symmetric synaptic interaction matrix of the Hopfield model enhances the overall accessibility of the memory states. The possibility of convergence to spurious fixed points is greatly reduced if a suitable upper limit is set to the convergence time. This prescription for suppressing convergence to spurious fixed points becomes more effective in the presence of asymmetry in synaptic interactions. The study of the one pattern model using the mean field Monte Carlo method provides useful information about the phase space structure in the parameter-space of the acquisition rate of the stored pattern. The presence of random asymmetry in the couplings results in better retrieval performance of the network by enhancing the size of the basin of attraction of the stored pattern and by making the recall of memory significantly faster.

   Studies on the Hopfield model with self-couplings reveal, contrary to Expectations, from some earlier studies states, that negative self-coupling causes deterioration in the retrieval performance of the network. On the other hand, it is possible to enhance the retrieval performance by having a positive self-coupling of appropriate magnitude.

   Few Related Publications:

   1. Fixed points in a Hopfield model with random asymmetric interactions
      M. P. Singh,  Zhang Chengxiang; C. Dasgupta, 
      Physical Review E:   Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 52 5261-72.  (1995).
      
      
   2. Hopfield model with self-coupling
      M. P. Singh,
      Physical Review E: Statistical, Nonlinear, and Soft Matter Physics. 64 51912-52001 (2001)
      
      
6. Quantum Optics and Nonlinear Optics

   Studied the dissipative dynamics of Jaynes-Cummings model in an optical cavity coupled to a broad band squeezed reservoir by solving the resulting master equation by Monte Carlo Wave Function method. It is shown that the squeezed vacuum can enhance the non-classical effects in cavity-QED systems, namely, the revival of atomic population and the generation of Shrodinger cat states. Carried out a theoretical analysis of the thermal defocussing optical limiter in the transient regime, i.e. when the laser pulse duration is comparable to the acoustic transit time, using a hydrodynamic theory. The general dependance of optical limiting strength on sample location, nonlinear phase change, and the relative pulse duration was obtained and found to be in good agreement with the available experimental results. Motivated by the recent non linear optical experiments on the non spherical nano-structures, developed a theoretical framework for calculating linear and nonlinear optical properties of a wedge shaped nano-structure. The general dependence of the linear polarizability and the second order hyperpolarizability on the radius and the apex angle of wedge is analyzed in detail. In particular, a very large enhancement in the second order hyperpolarizability is observed as the apex angle is reduced for the constant volume of the nano-structure.

   Few Related Publications

   1. “Analysis of the performance of a thermal defocusing optical limiter in the transient regime”,
      M. P. Singh and S. C. Mehendale,
      IEEE Journal of Quantum Electronics 34, 1867-72  (1998).
      
      
   2. “Dynamics of Jaynes-Cummings model in an optical cavity with injected   squeezed  vacuum”,
      M. P. Singh and A. Banerjee,
      Opt. Commun. 161, 243 (1999).
      
      
7. Non-linear Optics in In-organics:

   

   Gigantic optical nonlinearities are observed in various one dimensional Mott-Hubbard insulators represented by solid circles compared to other one dimensional materials (hollow circles). Experimental and theoretical research predicts occurrence of nearly degenerate one and two photon states in these one dimensional Mott-Hubbard insulators which are very strongly dipole coupled. This is the primary reason for huge ground state optical non-linearities like TPA, THG, EA. These materials are theoretically predicted to have orders-of-magnitude higher excited state optical nonlinearities in the wavelength region suitable for terahertz communications, strong stimulated raman stokes gain with possible application as THz source.

   Few Related References:

   • `` Excited state nonlinear optics of quasi-one-dimensional Mott-Hubbard insulators” , Haranath Ghosh, Physical Review B 75, 235127 , 2007 (and references therein).
   • ``Gigantic Stimulated Raman Scattering in one-dimensional Mott-Hubbard insulators : a possible THz source”, Haranath Ghosh and Rama Chari, in the proceedings of ”International conference on emerging trends in electronic and photonic devices and systems (ELECTRO-2009)”, December 22-24, 2009; McMillan Advanced Research series, p-155 .
   • ``Gaint ground and excited state optical nolinearty in one dimensional cuprates”, Haranath Ghosh, Europhys. Lett. 75(3) 468 2006.
   • "Quasi-one-dimensional copper oxide as a novel material with large room temperature ultrafast optical nonlinearity, Ogasawara T., Ashida M., Motoyama N., Eisaki H., Uchida S., Ghosh Haranath, Shukla A., Mazumdar S., Kuwata-Gonokami, Physical Review Letters, 85 , 2204, 2000.
     
     
8. Non-linear optics in Organics

   Most of the recent activities in conducting polymers is centered around their ability to emit light in the visible optical range. Though these materials are already commercialized, there is no concencus yet on the nature of light emitting excitons. Photoluminescent conjugated phenyl based polymers such as PPVs offer great potential in the next generation of optoelectronic devices. In addition, the quest for those organic molecules/polymers is on, which may possibly emit in the infrared --- Theory of infrared dye lasers. Many body calculations for various linear and non-linear properties of phenyl sustituted as well as phenyl based molecules such as poly di-phenyl accetylene (PDPA), ploy-phenyl accetylene (PPA), poly-para-phenylenevinylene (PPV), and Poly-para-phenylenes (PPP), aromatic diamines like N,N’-diphenyl-N,N’-bis(3-methylphenyl)-1,1-biphenyl-4.4 diamine (TPD), are of prime interest.
   
   Various mean field theories, Analytical many body techniques, Quantum Monte Carlo, Exact Diagonalization, Configuration Interaction, ab initio many body approaches are adopted  depending on the problem.
   
   Few Related References:

   • ``Ground and excited state nonlinear optics of Poly(-para phenylene vinylene), Haranath Ghosh, Synthetic Metals, 158, 320 (2008).
     
   • ``A possible route to the violation of Vavilob Kasha rule in π-conjugated polymers”, Haranath Ghosh, Chem. Phys. Lett. 426 (4-6) 431–435 (2006).
   • "Excited state absorptions in oligomers of PPV”, Haranath Ghosh, Synthetic Metals, 155, 439 (2005).
     "Theory of exited-state absorption in phenylene-based π-conjugated polymers", Shukla, A.; Ghosh, H.; Mazumdar, S. Physical Review B, 67, 245203-11, 2003.
     
     
9. Superconductivity and magnetism

   Studies on various phases of HTSCs like cuprates, Fe-based superconductors  are the most important studies of current condensed matter physics. There are similarities as well as dissimilarities in these two classes of superconductors e.g,  Fe-based superconductors   are multi-orbital in contrast to the cuprates. While cuprate superconductors are dominantly d-wave nature, the same is not yet established in case of  Fe-based superconductors. On the other hand, under certain conditions, the emission of cooper pairs from the surfaces of superconducting material  on the absorption of single photons in the vacuum ultraviolet range is possible.  Measured angular correlations of the photo-excited (Cooper) pairs can be related to the Cooper pair wave function in momentum space. Theoretical studies of double photo electron spectroscopy of various HTSCs are thus most authentic.

   Few Related References:

   • "Interplay of staggered flux phase and d-wave superconductivity", Haranath Ghosh and A. Singh, Physical Review B, 66 , 64530, 2002
   • "Stability of the doped antiferromagnetic state of the t-t-prime Hubbard model", A. Singh and Haranath Ghosh, Physical Review B, 65 , 134414, 2002.