We investigate nonequilibrium two-electron transfer in a model redox system represented by a two-site extended Hubbard model and embedded in a dissipative environment. The influence of the electron-electron interactions and the coupling to a dissipative bosonic bath on the electron transfer is studied in different temperature regimes. At high temperatures, Marcus transfer rates are evaluated, and at low temperatures, we calculate equilibrium and nonequilibrium population probabilities of the donor and acceptor with the nonperturbative numerical renormalization group approach. We obtain the nonequilibrium dynamics of the system prepared in an initial state of two electrons at the donor site and identify conditions under which the electron transfer involves one concerted two-electron step or two sequential single-electron steps. The rates of the sequential transfer depend nonmonotonically on the difference between the intersite and on-site Coulomb interaction, which become renormalized in the presence of the bosonic bath. If this difference is much larger than the hopping matrix element, the temperature as well as the reorganization energy, simultaneous transfer of both electrons between donor and acceptor can be observed.
In this work we investigate some aspects of the physics of strongly correlated systems by taking into account both electron-electron and electron-phonon interactions as basic mechanisms for reproducing electronic correlations in real materials. The relevance of the electron-electron interactions is discussed in the first part of this thesis in the framework of a self-consistent theoretical approach, named Composite Operator Method (COM), which accounts for the relevant quasi-particle excitations in terms of a set of composite operators that appear as a result of the modification imposed by the interactions on the canonical electronic fields. We show that the COM allows the calculation of all the relevant Green’s and correlation functions in terms of a number of unknown internal parameters to be determined self-consistently. Therefore, depending on the balance between unknown parameters and self-consistent equations, exact and approximate solutions can be obtained. By way of example, we discuss the application of the COM to the extended t-U- J-h model in the atomic limit, and to the two-dimensional single-band Hubbard model. In the former case, we show that the COM provides the exact solution of the model in one dimension. We study the effects of electronic correlations as responsible for the formation of a plethora of different charge and/or spin orderings. We report the phase diagram of the model, as well as a detailed analysis of both zero and finite temperature single-particle and thermodynamic properties. As far as the single-band Hubbard model is concerned, we illustrate an approximated selfconsistent scheme based on the choice of a two-field basis. We report a detailed analysis of many unconventional features that arise in single-particle properties, thermodynamics and system’s response functions. We emphasize that the accuracy of the COM in describing the effects of electronic correlations strongly relies on the choice of the basis, paving the way for possible multi-pole extensions to the twofield theory. To this purpose, we also study a three-field approach to the single-band Hubbard model, showing a significant step forward in the agreements with numerical data with respect to the two-pole results. The role of the electron-phonon interaction in the physics of strongly correlated systems is discussed in the second part of this thesis. We show that in highly polarizable lattices the competition between unscreened Coulomb and Fröhlich interactions results in a short-range polaronic exchange term Jp that favours the formation of local and light pairs of bosonic nature, named bipolarons, which condense with a critical temperature well in excess of hundred kelvins. These findings, discussed in the framework of the so-called polaronic t-Jp model, are further investigated in the presence of a finite on-site potential ~U , coming from the competition between on-site Coulomb and Fröhlich interactions. We discuss the role of ~U as the driving parameter for a small-to-large bipolaron transition, providing a possible explanation of the BEC-BCS crossover in terms of the properties of the bipolaronic ground state. Finally, we show that a hard-core bipolarons gas, studied as a charged Bose-Fermi mixture, allows for the description of many non Fermi liquid behaviours, allowing also for a microscopic explanation of pseudogap features in terms of a thermal-induced recombination of polarons and bipolarons, without any assumption on preexisting order or broken symmetries. [edited by Author]
We investigate vibrationally assisted electron transfer in an effective ligand--receptor complex using finite-temperature non-Markovian quantum-state diffusion with explicitly colored environmental noise. The model comprises donor and acceptor electronic states, an explicit bound-ligand vibrational mode, and a Gaussian protein--solvent bath. Linearization of a coordinate-dependent diabatic Hamiltonian yields two distinct system--environment interactions: diagonal coupling, which modulates the donor--acceptor energy gap, and off-diagonal non-Condon coupling, which modulates the electronic tunneling matrix element. In the rapidly equilibrating diagonal-bath limit, the model recovers the expected Marcus--Levich--Jortner vibronic-transfer behavior. Persistent environmental correlations instead generate non-exponential dynamics characterized by transient oscillations, back-transfer, and memory-dependent damping. Under matched weak-tunneling conditions, off-diagonal coupling opens a direct transition pathway and produces a larger finite-time acceptor population throughout the investigated parameter space. Because these dynamics do not generally support a unique kinetic rate, the enhancement is quantified using a time-averaged transfer yield. Comparisons with exact closed-system and commuting pure-dephasing limits validate the deterministic propagator and colored-noise construction, respectively, while the noncommuting dynamics are evaluated within a declared first-order finite-memory closure. These results identify ligand vibration, environmental memory, and non-Condon tunneling modulation as cooperating mechanisms that can dynamically regulate electron transfer in receptor-like environments, while maintaining a clear distinction between a mechanistic coarse-grained model and an atomistically parameterized biological complex.
Electronic Correlation in Molecules - Some Fundamental Problems Improving the Panoply of Quantum Chemical Methods for the Study of Correlated Extended Systems Lie-Algebraic Structure and the Coupled Cluster Method Configuration Interaction Studies Using Biorthogonal Approach to VB Basis Optimised Virtual Orbitals for the Calculation of Molecular Properties of Excited Electronic States A Novel MO-VB Scheme for Excitation Gaps in Correlated Mode Hamiltonians Correlated Approach to Molecular Properties Infinite Volume Extrapolations of Finite Clusters Calculations - How Correct are These? Calculation of the Hyperpolarisabilities of Organic Molecules and their Role in the Interpretation of Nonlinear Optical Phenomena in Organic Crystals Energy Thresholds in Polysilanes - Elementary Excitations of Alternating Conjugated Chains Inter- and Intramolecular Spin Coupling in Organics Electron Correlation Effects in Semiconductorquantum Dot Nanostructures Numerical Simulations of Strongly-Correlated Systems-Interlayer Tunnelling Mechanism, Spin-Charge Separation and Odd-Gap Pairing Metal Insulator Transition in 3rd Transition Metal Oxides Superconductivity in Doped Fullerenes.
We consider a model of TTF-TCNQ (tetrahiafulvalenium-tetracyanoquinodimethanide) and similar charge-transfer linear conductors in which there are two chains. The electrons on the acceptor (TCNQ) chains have a usual metallic band, but the electrons on the donor (TTF) chains have an inverted or "hole" band. The electrons on each chain interact via the forward and backward scattering
g2 and
g1 processes, respectively. Electrons on different chains interact via the analogous processes
W2 and
W1. The model is also applicable to two metallic chains, with the signs of
W1 and
W2 reversed. Using the techniques of Luther and Emery and of Chui and Lee we show that the problem may be mapped onto a similar problem of three coupled classical two-dimensional Coulomb gases. In addition to gaps in the spin degrees of freedom that were present in the single-chain problem, we find that the antisymmetric form of the resultant charge degrees of freedom may have a gap. We then investigate the predominant two-, four-, six-, and eight-particle response functions and calculate their temperature dependence. In addition to the four divergent two-particle response functions present in the single chain, there is a region for weak interaction strengths in which the
2kF interchain Cooper pairing response is the most divergent as $T\ensuremath{\rightarrow}0$. The excitonic insulator response may also be important at high temperatures. For the single chain, either the
4kF response or a four-particle
q=0 response is the most divergent for strong coupling and repulsive
g1, depending upon the sign of ${g}_{2}\ensuremath{-}\frac{1}{2}{g}_{1}$. For the two-chain system, the most divergent response as $T\ensuremath{\rightarrow}0$ for strongly attractive interactions (
g1 and
g2) is the response to the formation of excitonic "molecules" or exciton pairs. For strong coupling and repulsive
g1 either
8kF or octet responses may be observable. We discuss these results in conjunction with our previous renormalization-group treatment, which indicates that for certain values of
g2,
W2, and
W1 the line
g1=0 may be crossed. We use these results to interpret the recent x-ray data on TTF-TCNQ showing a crossover from
4kF to
2kF behavior above the crossover from one-dimensional to three-dimensional behavior.