Department of Physics, Tel: +44 (0) 1509 22 8409

John Samson's Research
 

Dr John (J H) Samson, CPhys MInstP, Senior Lecturer in Physics

Department of Physics, Loughborough University, Loughborough, Leics LE11 3TU, United Kingdom

Email: j.h.samson@lboro.ac.uk
Room number: W2.11 (Sir David Davies Building)
Telephone: +44 (0) 1509 22 3304 (Internal calls: dial last four digits only)
Fax: +44 (0) 1509 22 3986
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Research Interests


 

Electron-phonon interactions and superconductivity

Collaborators: Sasha Alexandrov, Jim Hague, Tom Hardy, Steven Jackson, Pavel Kornilovitch, Paul Spencer

The Holstein model describes interacting electrons coupled to optic phonons. A continuous-time quantum Monte Carlo (CTQMC) algorithm was used to investigate the kinetic and potential energy, effective mass and isotope exponent of a lattice polaron in one dimension with various forms of electron-phonon interaction (EPI). This work was extended through an EPSRC grant Polaron Dynamics and Isotope Effects In Complex Oxides. Here we investigated polarons in one, two and three dimensions with a variety of interaction ranges, and studied the properties of bipolarons. With strong on-site repulsion between electrons and a long-range EPI, electrons can form local pairs (small bipolarons). We have calculated the effective mass of such pairs both by CTQMC and by analytical mapping of the pairs onto an effective dimer lattice. These pairs are very mobile on a triangular lattice, since pair hopping can occur by single-particle hops, indicating the possibility of a high transition temperature. In related work, variational Monte Carlo calculations on a two-dimensional Hubbard-Fröhlich model (on-site repulsion and long-range EPI) show that EPI enhances the tendency for d-wave order, which may be absent in a pure Hubbard model.

Publications and preprints in this area

  1. Continuous-time quantum Monte Carlo studies of lattice polarons, P E Spencer, PhD thesis, Loughborough University (2000)
  2. Effect of electron-phonon interaction range on lattice polaron dynamics: a continuous-time quantum Monte Carlo study, P E Spencer, J H Samson, P E Kornilovitch and A S Alexandrov, Phys RevB71 184310 (19) (2005) and cond-mat/0407250
  3. Effects of lattice geometry and interaction range on polaron dynamics, J P Hague, P E Kornilovitch, A S Alexandrov and J H Samson, Phys Rev B73 054303 (14) (2006), erratum B75 059901(E)(2) (2007) and cond-mat/0509059
  4. Superlight small bipolarons in the presence of a strong Coulomb repulsion, J P Hague, P E Kornilovitch, JHS and A S Alexandrov, Phys Rev Lett 98 037002 (4) (2007)
  5. Superlight small bipolarons, J P Hague, P E Kornilovitch, JHS and A S Alexandrov, J Phys: Condens Matter 19 255214 (26) (2007)
  6. Superconductivity in a Hubbard-Fröhlich Model and in cuprates, submitted to Phys Rev B, arXiv:0806.2810

The Wigner function and other quasiprobabilities in quantum mechanics

Collaborators: Neil Lindsey


A quantum system can be modelled by an equivalent classical system, at the cost of a non-positive distribution for the classical variables. Examples include the Wigner function (a joint distribution for non-commuting variables), the violation of the Bell inequalities between correlations in an entangled state, and the notorious Monte Carlo sign problem. The latter provided the motivation for this programme. The Monte Carlo approach to statistical mechanics simulates a physical system by generating configurations at random with specified probabilities. A serious difficulty hampering application to quantum many-body systems is the sign problem: quantities that should represent probabilities can become negative or complex. Calculations can still be performed in principle, but involve differences between large positive numbers of similar magnitude and are numerically unstable. As the method is widely used in numerical studies of high-temperature superconductors, an understanding of the source of this difficulty is of great importance.This work has interpreted the sign problem as a manifestation of the Berry phase, the geometrical phase factor that arises when a quantum state is transported round a closed path, and as a consequence of the Wigner function. This occurs when the simulation is trying to generate a distribution for non-commuting variables, such as the components of a spin. The sign problem is then a consequence of the uncertainty principle: the simulation is asking impermissible questions of incompatible variables in a quantum system, such as components of the spin of a single electron. I have shown, both analytically and numerically, how the Wigner function emerges as interference fringes of the Berry phase of paths in a path integral. The effect of finite discretisation of paths, an essential prerequisite of a Monte Carlo simulation, has also been investigated. Finite-discretisation approximants may have unphysical properties such as negative heat capacity and negative density of states. We are investigating the application of path integration to the calculation of Wigner functions.

Publications in this area

  1. Functional integration and quantum Monte Carlo in itinerant magnets: the Berry phase and the sign problem. J H Samson, International Conference on the Physics of Transition Metals, Darmstadt, Int J Mod Phys B7 (1993) 593-596
  2. Quantum Monte Carlo computation: the sign problem as a Berry phase. J H Samson, Phys Rev B47 (1993) 3408-3411
  3. Aspects of the sign problem . J H Samson, in Quantum Monte Carlo Methods in Condensed Matter Physics , ed M Suzuki 235-250 (World Scientific, 1993)
  4. Classical effective Hamiltonians, Wigner functions and the sign problem. J H Samson, Strongly Correlated Electron Systems, Amsterdam, Physica B206-207 (1995) 163-165
  5. Functional integration in itinerant magnets: what does it mean? J H Samson, International Conference on Magnetism, Warszawa, J Magn Magn Mater 140-144 (1995) 203-204
  6. Classical effective Hamiltonians, Wigner functions, and the sign problem. J H Samson, Phys Rev B51 (1995) 223-233
  7. Auxiliary fields and the sign problem. J H Samson, Int J Mod Phys C (Physics and Computers) 6 (1995) 427-465
  8. Exact classical effective potentials. J H Samson, Proceedings of Sixth International Conference on Path Integrals from peV to TeV, Firenze, August 1998, edited by R. Casalbuoni et al (World Scientific, Singapore, 1999) 550-553
  9. Coherent-state path integral calculation of the Wigner function , J Phys A: Math Gen 33 (2000) 5129-5229
  10. Time discretization of functional integrals, J Phys A: Math Gen 33 (2000) 3111-3120
  11. Phase-space path-integral calculation of the Wigner function, J Phys A: Math Gen 36,10637-10650 (2003)
  12. Path integral calculation of the Wigner function, N Lindsey, PhD thesis, Loughborough University (2009)
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Adiabatic quantum computing

Many optimisation problems can be encoded by an Ising Hamiltonian, where the energy corresponds to the cost function of the problem. Finding the ground state of a frustrated Ising model is in general an NP-hard problem, with an exponentially large number of local minima. Thus classical annealing algorithms would take an exponentially long time to find the ground state. It has been proposed that application of a large transverse field, which is then slowly turned off so that the system remains close to the instantaneous ground state, would result in a faster approach to at least an approximate ground state. Effectively the system tunnels between the local minima. Research projects available in this area.

 

Hartree-Fock solutions of the Hubbard model

Collaborators: Z B Asghar, F V Kusmartsev, A Radosz


The Hartree-Fock phase diagram of the one-dimensional Hubbard model throws light on a number of issues in two and three dimensions. The results are relevant to the existence of collinear versus non-collinear spin density waves in solids. They also show evidence of phase separation, which may be related to the formation of a soliton lattice or to stripe phases. The phase diagram of uniform states (those without local charge density modulation, but with possible phase separation). Current work is related to the application of similar techniques to the study of localised distortions in photoinduced phases.

Publications in this area

  1. Spin density waves in the 1D Hubbard model. J H Samson, International Conference on Magnetism, Warszawa, J Magn Magn Mater 140-14 (1995)4 205-206
  2. Spin density wave selection in the one-dimensional Hubbard model. J H Samson, J Phys: Condensed Matter 8 (1996) 569-580
  3. Phase Separation in the Hubbard model. J H Samson, Proceedings of Physics of Magnetism 96, Acta Physica Polonica A92 (1997) 363-366
  4. Spin density waves in the Hubbard model, Z B Asghar, PhD thesis, Loughborough University (2001)
  5. Lattice multi-stability in low-dimensional structures. A Radosz, K Ostasiewicz, P Magnuszewski, L Radosiñski, F V Kusmartsev and J H Samson, Phys Stat Sol (b) 242 303–310 (2005)
  6. Electron-phonon coupling in photo-induced phase transitions. A Radosz, K Ostasiewicz, P Magnuszewski, L Radosiñski, F V Kusmartsev and J H Samson, Phys Stat Sol (b) 242 454–460 (2005)
  7. Thermodynamics of entropy-driven phase transformations. A Radosz, K Ostasiewicz, P Magnuszewski, J Damczyk, L Radosiñski, F V Kusmartsev, JHS, A C Mitus and G Pawlik, Phys Rev E73 026127 (15) (2006)


Fourier kernels

Collaborators: G A Evans


In computing Fourier transforms of functions of several variables invariant under some symmetry, it is useful to integrate over the symmetry group (analytically if possible) to leave an integral over the invariants. For example, one might require the momentum-space wave function of an N-electron atom given a real-space wave function invariant under rigid rotation of the electron coordinates. This is a generalisation of the well-known Hankel transform, and does not seem to have been discussed previously in the literature. For N vectors in three dimensions the kernel reduces to a one-dimensional integral involving Bessel functions; for N=2 this becomes a one-dimensional integral of elementary functions. Methods of dealing numerically with this integral have been studied.

Publications in this area

  1. Symmetry reduction of Fourier kernels, J H Samson and G A Evans, J Comput Phys 142 (1998) 109-122

 

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