Eldorado Collection:
http://hdl.handle.net/2003/25414
2024-06-18T18:32:52ZQuantum integrability and non-integrability in the spin-boson model
http://hdl.handle.net/2003/25463
Title: Quantum integrability and non-integrability in the spin-boson model
Authors: Stolze, Joachim; Stepanov, Vyacheslav V.; Müller, Gerhard2008-06-04T00:00:00ZDynamic properties of the spin-1/2 XX chain with three-spin interactions
http://hdl.handle.net/2003/25462
Title: Dynamic properties of the spin-1/2 XX chain with three-spin interactions
Authors: Stolze, Joachim; Verkholyak, Taras; Derzhko, Oleg; Krokhmalskii, Taras
Abstract: We consider a spin-(1/2) XY chain in a transverse (z) field with multisite interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan–Wigner transformation leads to a simple bilinear Fermi form for the resulting Hamiltonian and, hence, the spin model admits a rigorous analysis. We point out the close relationships between several variants of the model, which were discussed separately in previous studies. The ground-state phases (ferromagnet and two kinds of spin liquid) of the model are reflected in the dynamic structure factors of the spin chains, which are the main focus in this study. First, we consider the zz dynamic structure factor, reporting for this quantity a closed-form expression and analyzing the properties of the two-fermion (particle-hole) excitation continuum, which governs the dynamics of transverse spin component fluctuations and of some other local operator fluctuations. Then we examine the xx dynamic structure factor, which is governed by many-fermion excitations, reporting both analytical and numerical results. We discuss some easily recognized features of the dynamic structure factors, which are signatures of the presence of the three-site interactions.2008-05-02T00:00:00ZSpin-1/2 XX Chains with Three-Spin Interactions
http://hdl.handle.net/2003/25461
Title: Spin-1/2 XX Chains with Three-Spin Interactions
Authors: Stolze, Joachim; Verkholyak, Taras; Derzhko, Oleg; Krokhmalskii, Taras
Abstract: We consider a spin-1/2 XX chain with three-spin interactions which is equivalent to a system of noninteracting spinless fermions.We examine some dynamic quantities of the spin model.In particular, we calculate analytically the dynamic transverse (zz) structure factor which is governed by a two-fermion excitation continuum. Moreover, we compute numerically the dynamic xx structure factor which is a many-fermion dynamic quantity.We illustrate how the three-spin interactions manifest themselves in the dynamic probes.2008-01-01T00:00:00ZDynamic correlations in a random spin-1/2 XY chain
http://hdl.handle.net/2003/25460
Title: Dynamic correlations in a random spin-1/2 XY chain
Authors: Stolze, Joachim; Verkholyak, Taras; Derzhko, Oleg; Krokhmalskii, Taras
Abstract: We examine dynamic quantities of a random spin-1/2 isotropic XY chain in a transverse field. The randomness is related to the sign of the nearest-neighbor exchange interaction and can be eliminated by a suitable transformation. As a result, the dynamic quantities for the random spin chain are related to the same dynamic quantities for the homogeneous spin chain. We use the available results for the latter model to discuss the effect of randomness on the dynamic structure factors of the quantum spin chain.2008-01-01T00:00:00ZSpin- and entanglement-dynamics in the central-spin model with homogeneous couplings
http://hdl.handle.net/2003/25459
Title: Spin- and entanglement-dynamics in the central-spin model with homogeneous couplings
Authors: Stolze, Joachim; Bortz, Michael
Abstract: We calculate exactly the time-dependent reduced density matrix for the central spin in the central-spin model with homogeneous Heisenberg couplings. Therefrom, the dynamics and the entanglement entropy of the central spin are obtained. A rich variety of behaviours are found, depending on the initial state of the bath spins. For an initially unpolarized unentangled bath, the polarization of the central spin decays to zero in the thermodynamic limit, while its entanglement entropy becomes maximal. On the other hand, if the unpolarized environment is initially in an eigenstate of the total bath spin, the central spin and the entanglement entropy exhibit persistent monochromatic large-amplitude oscillations. This raises the question of to what extent entanglement of the bath spins prevents decoherence of the central spin.2007-01-01T00:00:00ZExact dynamics in the inhomogeneous central-spin model
http://hdl.handle.net/2003/25458
Title: Exact dynamics in the inhomogeneous central-spin model
Authors: Stolze, Joachim; Bortz, Michael
Abstract: We study the dynamics of a single spin 1/2 coupled to a bath of spins 1/2 by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for the dynamics of the central spin is presented, based on the Bethe ansatz. For initially completely polarized bath spins and small magnetic field, we find persistent oscillations of the central spin about a nonzero mean value. For a large number of bath spins Nb, the oscillation frequency is proportional to Nb, whereas the amplitude behaves as 1/Nb, to leading order. No asymptotic decay of the oscillations due to the nonuniform couplings is observed, in contrast to some recent studies.2007-07-26T00:00:00ZDynamic properties of quantum spin chains
http://hdl.handle.net/2003/25457
Title: Dynamic properties of quantum spin chains
Authors: Stolze, Joachim; Verkholyak, Taras; Derzhko, Oleg; Krokhmalskii, Taras2007-10-15T00:00:00ZDynamics of quantum spin chains and multi-fermion excitation continua
http://hdl.handle.net/2003/25456
Title: Dynamics of quantum spin chains and multi-fermion excitation continua
Authors: Stolze, Joachim; Derzhko, Oleg; Krokhmalskii, Taras; Müller, Gerhard2006-02-17T00:00:00ZDimer and Trimer fluctuations in the s=1/2 transverse XX chain
http://hdl.handle.net/2003/25455
Title: Dimer and Trimer fluctuations in the s=1/2 transverse XX chain
Authors: Stolze, Joachim; Derzhko, Oleg; Krokhmalskii, Taras; Müller, Gerhard2005-01-01T00:00:00ZSpin Chains as Perfect Quantum State Mirrors
http://hdl.handle.net/2003/25454
Title: Spin Chains as Perfect Quantum State Mirrors
Authors: Stolze, Joachim; Karbach, Peter
Abstract: Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions that display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics, any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at an arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.2005-01-01T00:00:00ZMultiparticle entanglement and ranks of density matrices
http://hdl.handle.net/2003/25453
Title: Multiparticle entanglement and ranks of density matrices
Authors: Stolze, Joachim; Chong, Bo; Keiter, Hellmut
Abstract: Based on the ranks of reduced density matrices, we derive necessary conditions for the separability of multiparticle arbitrary-dimensional mixed states, which are equivalent to sufficient conditions for entanglement. In a similar way we obtain necessary conditions for the separability of a given mixed state with respect to partitions of all particles of the system into subsets. The special case of pure states is discussed separately.2005-01-01T00:00:00ZDynamics of alternating spin chains
http://hdl.handle.net/2003/25452
Title: Dynamics of alternating spin chains
Authors: Stolze, Joachim; Derzhko, Oleg; Krokhmalskii, Taras2002-02-01T00:00:00ZDynamic properties of the dimerized spin-1/2 isotropic XY chain in a transverse field
http://hdl.handle.net/2003/25451
Title: Dynamic properties of the dimerized spin-1/2 isotropic XY chain in a transverse field
Authors: Stolze, Joachim; Derzhko, Oleg; Krokhmalskii, Taras
Abstract: The zz and xx(yy) dynamic structure factors of the dimerized spin-½ isotropic XY chain in a transverse (z) field are calculated for arbitrary temperatures. The zz structure factor can be given in analytical terms, involving a single integration, whereas the xx dynamic structure factor can be evaluated completely numerically for very long chains. We compare the two structure factors and discuss in some detail how a dimerization manifests itself in the dynamic structure factors at different external fields and temperatures. We compare our results to corresponding results for the dimerized Heisenberg chain obtained by approximate techniques.2002-04-26T00:00:00ZDisorder Induced Quantum Phase transitions in Random-Exchange Spin-1/2 Chains
http://hdl.handle.net/2003/25450
Title: Disorder Induced Quantum Phase transitions in Random-Exchange Spin-1/2 Chains
Authors: Stolze, Joachim; Hamacher, Kay; Wenzel, Wolfgang
Abstract: We investigate the effect of quenched bond disorder on the anisotropic antiferromagnetic spin-1/2 (XXZ) chain as a model for disorder-induced quantum phase transitions. We find nonuniversal behavior of the average correlation functions for weak disorder, followed by a quantum phase transition into a strongly disordered phase with only short-range xy correlations. We find no evidence for the universal strong-disorder fixed point predicted by the real-space renormalization group, suggesting a qualitatively different view of the relationship between quantum fluctuations and disorder.2002-08-28T00:00:00ZImpurity spin relaxation in S=1/2 XX chains
http://hdl.handle.net/2003/25449
Title: Impurity spin relaxation in S=1/2 XX chains
Authors: Stolze, Joachim; Vogel, Michael2000-01-01T00:00:00ZDynamics of the spin-1/2 isotropic XY chain in a transverse field
http://hdl.handle.net/2003/25448
Title: Dynamics of the spin-1/2 isotropic XY chain in a transverse field
Authors: Stolze, Joachim; Derzhko, Oleg; Krokhmalskii, Taras2000-04-28T00:00:00ZNumerical evaluation of coherent-state path integrals in quantum dynamics
http://hdl.handle.net/2003/25447
Title: Numerical evaluation of coherent-state path integrals in quantum dynamics
Authors: Stolze, Joachim; Burghardt, Bernd
Abstract: The numerical evaluation of coherent-state path integrals for quantum dynamical problems is discussed for one-dimensional examples. To propagate an initial state, we use the normal and antinormal ordered coherent-state path integrals combined with a split-operator technique dividing the Hamiltonian into harmonic and anharmonic parts. For numerical purposes integrations must be approximated by quadrature formulae. This leads to a matrix multiplication scheme which is systematically tested for the double-well and Morse potentials. The method is accurate for propagation times much longer than the natural time scale of the system, and it allows for short as well as long time steps without loss of stability.1999-03-19T00:00:00ZNumerical evaluation of coherent-state path integrals with application to time-dependent problems
http://hdl.handle.net/2003/25446
Title: Numerical evaluation of coherent-state path integrals with application to time-dependent problems
Authors: Stolze, Joachim; Burghardt, Bernd
Abstract: We study the application of the coherent-state path integral as a numerical tool for wave-packet propagation. The numerical evaluation of path integrals is reduced to a matrix-vector multiplication scheme. Together with a split-operator technique we apply our method to a time-dependent double-well potential.1999-01-01T00:00:00ZEvaluation of coherent-state path integrals in statistical mechanics by matrix multiplication
http://hdl.handle.net/2003/25445
Title: Evaluation of coherent-state path integrals in statistical mechanics by matrix multiplication
Authors: Stolze, Joachim; Burghardt, Bernd; Eicke, Joachim
Abstract: The numerical evaluation of coherent-state path-integral representations for partition functions and other quantities in equilibrium quantum statistical mechanics is discussed. Several coherent-state path-integral schemes are introduced, which differ from each other by the order of approximation and by the operator ordering employed in the high-temperature approximation of the density operator. Simple one-dimensional systems are used to test these schemes. For the harmonic oscillator, finite-dimensional approximations to the coherent-state path integral are calculated analytically and compared to each other and to the real-space path integral. For anharmonic systems, integrations must be approximated by quadrature formulas. This leads to a matrix multiplication scheme which is tested for the double-well potential. The results obtained are accurate from zero temperature way up into the high-temperature regime where quantum effects become negligible. This is a significant advantage over traditional real-space path integral schemes which break down at low temperatures.1998-01-22T00:00:00ZDynamic correlations of antiferromagnetic spin- XXZ chains at arbitrary temperature from complete diagonalization
http://hdl.handle.net/2003/25444
Title: Dynamic correlations of antiferromagnetic spin- XXZ chains at arbitrary temperature from complete diagonalization
Authors: Stolze, Joachim; Fabricius, Klaus; Löw, Ute1997-01-01T00:00:00ZCharge and spin dynamics in the one-dimensional t-J_z and t-J models
http://hdl.handle.net/2003/25443
Title: Charge and spin dynamics in the one-dimensional t-J_z and t-J models
Authors: Stolze, Joachim; Zhang, Shu; Müller, Gerhard; Karbach, Michael1997-01-01T00:00:00ZSpin correlation functions in random-exchange s=1/2 XXZ chains
http://hdl.handle.net/2003/25442
Title: Spin correlation functions in random-exchange s=1/2 XXZ chains
Authors: Stolze, Joachim; Röder, Heinrich; Silver, Richard N.; Müller, Gerhard1996-04-15T00:00:00ZImpact of criticality and phase separation on the spin dynamics of the one-dimensional t-J model
http://hdl.handle.net/2003/25441
Title: Impact of criticality and phase separation on the spin dynamics of the one-dimensional t-J model
Authors: Stolze, Joachim; Zhang, Shu; Müller, Gerhard1996-04-15T00:00:00ZEquation of motion approach to the Hubbard model in infinite dimensions
http://hdl.handle.net/2003/25439
Title: Equation of motion approach to the Hubbard model in infinite dimensions
Authors: Stolze, Joachim; Gros, Claudius; Wenzel, Wolfgang; Valentí, Roser1995-05-01T00:00:00ZZero-temperature dynamics of the one-dimensional XXZ and t-J models
http://hdl.handle.net/2003/25438
Title: Zero-temperature dynamics of the one-dimensional XXZ and t-J models
Authors: Stolze, Joachim; Viswanath, V. S.; Zhang, Shu; Müller, Gerhard1995-01-01T00:00:00ZGaussian, exponential, and power-law decay of time-dependent correlation functions in quantum spin chains
http://hdl.handle.net/2003/25437
Title: Gaussian, exponential, and power-law decay of time-dependent correlation functions in quantum spin chains
Authors: Stolze, Joachim; Nöppert, Angela; Müller, Gerhard1995-01-01T00:00:00ZThe Mott-Hubbard transition an the D = infinity Bethe lattice
http://hdl.handle.net/2003/25436
Title: The Mott-Hubbard transition an the D = infinity Bethe lattice
Authors: Stolze, Joachim; Gros, Claudius; Wenzel, Wolfgang; Valentí, Roser; Hülsenbeck, Georg1994-08-01T00:00:00ZSpin diffusion in the one-dimensional s=1/2 XXZ model at infinite temperature
http://hdl.handle.net/2003/25433
Title: Spin diffusion in the one-dimensional s=1/2 XXZ model at infinite temperature
Authors: Stolze, Joachim; Böhm, Markus; Viswanath, V. S.; Müller, Gerhard1994-01-01T00:00:00ZDynamical properties of quantum spin systems in magnetically ordered product ground states
http://hdl.handle.net/2003/25432
Title: Dynamical properties of quantum spin systems in magnetically ordered product ground states
Authors: Stolze, Joachim; Viswanath, V. S.; Müller, Gerhard
Abstract: The one-dimensional spin-s XYZ model in a magnetic field of particular strength has a ferro- or antiferromagnetically ordered product ground state. The recursion method is employed to determine T=0 dynamic structure factors for systems with s=1/2, 1, 3/2. The line shapes and peak positions differ significantly from the corresponding spin-wave results, but their development for increasing values of s suggests a smooth extrapolation to the spin-wave picture.1994-05-15T00:00:00ZDynamics of the one-dimensional spin-1 Heisenberg antiferromagnet with exchange and single-site anisotropy
http://hdl.handle.net/2003/25431
Title: Dynamics of the one-dimensional spin-1 Heisenberg antiferromagnet with exchange and single-site anisotropy
Authors: Stolze, Joachim; Zhang, Shu; Yu, Yongmin1994-05-15T00:00:00ZOrdering and fluctuations in the ground state of the one-dimensional and two-dimensional S=1/2 XXZ antiferromagnets
http://hdl.handle.net/2003/25430
Title: Ordering and fluctuations in the ground state of the one-dimensional and two-dimensional S=1/2 XXZ antiferromagnets
Authors: Stolze, Joachim; Viswanath, V. S.; Zhang, Shu; Müller, Gerhard1994-01-01T00:00:00ZSpectral signature of quantum spin diffusion in dimensions d=1, 2, and 3
http://hdl.handle.net/2003/25429
Title: Spectral signature of quantum spin diffusion in dimensions d=1, 2, and 3
Authors: Stolze, Joachim; Böhm, Markus; Leschke, Hajo; Henneke, Martin; Viswanath, V. S.; Müller, Gerhard1994-01-01T00:00:00ZDynamics of semi-infinite quantum spin chains at T=∞
http://hdl.handle.net/2003/25428
Title: Dynamics of semi-infinite quantum spin chains at T=∞
Authors: Stolze, Joachim; Viswanath, V. S.; Müller, Gerhard1992-02-01T00:00:00ZLower Bounds for the Ground-State Energies of the 2D Hubbard and t-J Models
http://hdl.handle.net/2003/25427
Title: Lower Bounds for the Ground-State Energies of the 2D Hubbard and t-J Models
Authors: Stolze, Joachim; Valentí, Roser; Hirschfeld, Peter J.
Abstract: We present simple lower bounds on the ground-state energy of the two-dimensional (2D) Hubbard and t-J models for arbitrary values of band filling and coupling constant. For the Hubbard model we derive two types of bounds, both based on decomposing the model Hamiltonian into a sum of sub-Hamiltonians. For a decomposition into local cluster sub-Hamiltonians, we perform a generalized Legendre transform on previously derived bounds for the grand-canonical potential. For a decomposition into spin-up and spin-down parts, previous results on the spinless Falicov-Kimball model may be used to obtain bounds for the Hubbard model, generalizing a result of Langer and Mattis to arbitrary filling. For the 2D t-J model we have only considered the decomposition into clusters. The 1D Hubbard model is used as a test case. The bounds may be improved by diagonalizing the Hamiltonian for larger clusters.1991-01-01T00:00:00ZClassical and quantum phase-space behavior of a spin-boson system
http://hdl.handle.net/2003/25426
Title: Classical and quantum phase-space behavior of a spin-boson system
Authors: Stolze, Joachim; Müller, Lothar; Leschke, Hajo; Nagel, Peter
Abstract: We study the phase-space behavior of the standard two-level system (spin 1/2) coupled to a harmonic oscillator (without the rotating-wave approximation), the classical counterpart of which is known to display deterministic chaos. We study the quantum-mechanical phase-space behavior by means of harmonic-oscillator coherent states (Husimi representation). Stationary quantum Poincaré sections may be defined; they show many parallels to their classical counterparts. We also study the time development of initially coherent states and observe a tendency towards a decay into many small wave packets in phase space for parameters in the chaotic regime.1990-01-01T00:00:00ZQuality of variational ground states for a two-state system coupled to phonons
http://hdl.handle.net/2003/25425
Title: Quality of variational ground states for a two-state system coupled to phonons
Authors: Stolze, Joachim; Müller, Lothar
Abstract: We generalize the variational approach proposed by Chen, Zhang, and Wu [Phys. Rev. B 40, 11 326 (1989)] to the ground state of a two-level system coupled to a single boson mode. The resulting displaced-squeezed state is compared to the true ground state (calculated numerically), and to further variational states, by computing energy differences and overlaps. These states are able to describe a bifurcation occurring in the ground state of the quantum system as well as in the equilibrium state of its classical limit, and they are excellent approximations to the true ground state.1990-01-01T00:00:00ZOxygen ordering in the basal plane of YBa2Cu3Oz
http://hdl.handle.net/2003/25424
Title: Oxygen ordering in the basal plane of YBa2Cu3Oz
Authors: Stolze, Joachim
Abstract: The ground-state configurations of a lattice-gas model introduced by de Fontaine, Wille, and Moss for the distribution of empty and occupied oxygen sites in the Cu-O basal plane of the high-temperature superconductor YBa2Cu3Oz are determined. It is shown rigorously that the configurations proposed earlier by Wille and de Fontaine basically exhaust the set of possible stable ground-state structures. States of partial order are excluded, except for special values of the interaction constants.1990-01-01T00:00:00ZConvergence properties of Coherent State Path Integrals from Statistical Mechanics
http://hdl.handle.net/2003/25423
Title: Convergence properties of Coherent State Path Integrals from Statistical Mechanics
Authors: Stolze, Joachim
Abstract: Coherent state path integral representations for matrix elements of density operators are compared to various formulations of coordinate space path integrals discussed recently [R. D. Coalson, J. Chem. Phys. 85, 926 (1986)]. The convergence properties of finite-dimensional approximations to these path integrals are tested for the harmonic oscillator. It is found that at low temperatures the coherent state path integrals converge much better than the coordinate space path integrals and thus should be preferred in numerical (e.g., Monte Carlo) calculations of low-temperature properties.1987-09-15T00:00:00ZOn Mean Field Theories of Singlet Superconductivity in Extended Hubbard Models
http://hdl.handle.net/2003/25422
Title: On Mean Field Theories of Singlet Superconductivity in Extended Hubbard Models
Authors: Stolze, Joachim
Abstract: Hubbard models extended by attractive interactions between nearest neighbours have recently been discussed as models for heavy fermion superconductivity. Here, a comparison is carried through between mean field calculations at finite band width and exact results on ground state properties in the atomic limit (i.e. at zero band width). It turns out that the mean field approximation does not provide an appropriate description of the ground state of the system. This holds true for arbitrary band filling. For half-filled band, an extended mean field approximation is studied, allowing for both antiferromagnetism and (singlet) superconductivity. It is found that these two types of order do not coexist within mean field theory.1986-06-01T00:00:00ZGround states of the Triangular Ising model with two-and three-spin interactions
http://hdl.handle.net/2003/25421
Title: Ground states of the Triangular Ising model with two-and three-spin interactions
Authors: Stolze, Joachim; Brandt, Uwe
Abstract: The possible ground state spin configurations of an Ising model on a plane triangular lattice are investigated. The model incorporates competing interactions between spins at nearest and next-nearest neighbour sites as well as a coupling between three spins at the vertices of a nearest-neighbour triangle, and an external magnetic field. Models of this type are frequently used to describe the structures of adsorbate layers on hexagonal substrates. The analysis is based on linear inequalities involving the magnetization, two- and three-spin correlations, and on simple convexity arguments. Part of the inequalities needed are proved with the aid of a computer. For vanishing three-spin coupling the results of earlier studies are confirmed; in addition, the resulting seven topologically distinct structures are shown to be unique. Two of these structures are energetically degenerate; the degeneracy cannot be lifted by any further two-spin interaction. For nonzero three-spin coupling only an "almost complete" solution is given, involving four additional spin configurations. The "ground state phase diagrams" are discussed.1986-11-01T00:00:00ZHigh-temperature dynamics of the anisotropic Heisenberg chain studied by moment methods
http://hdl.handle.net/2003/25420
Title: High-temperature dynamics of the anisotropic Heisenberg chain studied by moment methods
Authors: Stolze, Joachim; Brandt, Uwe
Abstract: The dynamics of the anisotropic spin-l/2 nearest-neighbour Heisenberg chain is studied at infinite temperature. Low-order coefficients of the short-time expansions are computed for spin-spin and energy-density-energy-density correlation functions for cyclical as well as for open-ended chains. The commutator algebra necessary to generate these coefficients may be performed by a computer. The series obtained for the spin correlation function (up to order t^14 for a bulk spin and up to order t^18 for a boundary spin) and for the energy density correlation function are the longest ones available up to now. The coefficients are used to construct rigorous upper and lower bounds to autocorrelation functions and near-neighbour correlation functions.1986-09-01T00:00:00ZGround states of extended Hubbard models in the atomic limit
http://hdl.handle.net/2003/25419
Title: Ground states of extended Hubbard models in the atomic limit
Authors: Stolze, Joachim; Brandt, Uwe
Abstract: The possible ground states of an extended Hubbard model in the atomic limit, augmented by an additional nearest neighbour Ising-like interaction and an external magnetic field, are rigorously determined for arbitrary values of the coupling parameters and arbitrary chemical potential. The method used requires only simple convexity arguments and the examination of all possible configurations of small clusters of lattice sites, which may be done by computer. The results are valid for all lattices ofAB type (two interpenetrating sublattices). The type of order found are ferromagnetic, antiferromagnetic, and charge density wave. Perturbation theory suggests that for finite band width there may be a state showing both a charge density wave and ferromagnetic order.1986-12-01T00:00:00ZOn the Validity of Certain Variational Principles for the Free Energy
http://hdl.handle.net/2003/25418
Title: On the Validity of Certain Variational Principles for the Free Energy
Authors: Stolze, Joachim1985-01-01T00:00:00ZThermodynamics of the molecular polaron
http://hdl.handle.net/2003/25417
Title: Thermodynamics of the molecular polaron
Authors: Stolze, Joachim; Brandt, Uwe
Abstract: The thermodynamics of the molecular polaron model-a two-level system coupled to a harmonic oscillator-is studied. Close upper and lower bounds to the free energy are derived by means of Tchebycheff-Markov inequalities and are compared with the results of other authors. The 'nearly free' behaviour for high temperatures is confirmed. The self-trapping effects at low temperatures are weaker than predicted earlier. In contrast to the prediction of mean-field theory, the transition between the two temperature regimes is not a sharp phase transition but rather a smooth crossover.1983-10-20T00:00:00ZA new hierarchy of upper and lower bounds on expectation values
http://hdl.handle.net/2003/25416
Title: A new hierarchy of upper and lower bounds on expectation values
Authors: Stolze, Joachim; Brandt, Uwe
Abstract: Upper and lower bounds are constructed for expectation values of functions of a real random variable with derivatives up to orderN+1 which are alternately negative and positive over the whole range of interest. The bounds are given by quadrature formulas with weights and abscissas determined by the firstN+1 moments of the underlying probability distribution. Application to a simple disordered phonon system yields sharp bounds on the specific heat.1981-03-01T00:00:00ZUnity-resolving states and generalised Golden-Thompson bounds on partition functions
http://hdl.handle.net/2003/25415
Title: Unity-resolving states and generalised Golden-Thompson bounds on partition functions
Authors: Stolze, Joachim; Leschke, Hajo; Moraweck, Michael
Abstract: It is shown that certain sets of normalised unity-resolving (e.g. coherent) states in Hilbert space serve to generate upper bounds on the partition function of a given Hamiltonian in that space. These bounds may be viewed as generalisations of bounds derived previously by Golden, Thompson, Hepp and Lieb (see Phys. Rev. A, vol.8, p.2517, 1973). The new bounds are compared to the original Golden-Thompson bound by proving several theorems and by computing explicit examples.1980-04-01T00:00:00Z