Excess heat in the Fleischmann–Pons experiment occurs without commensurate energetic nuclear radiation, which motivated us to seek mechanisms capable of fractionating a large quantum, resulting in the lossy spin-boson model. Collimated x-ray emission in the Karabut experiment we interpreted as demonstrating the conversion of vibrational energy to nuclear excitation, as predicted from the lossy spin-boson model; this motivated us to seek physical models that could account for the effect. We found that the coupling strength associated with electron–nuclear and electron–electron coupling was too weak to fractionate keV quanta into 100 MHz vibrations, which motivated us to seek a theory in which nuclear transitions coupled directly to vibrations. These considerations led us to a lattice model with a relativistic description of compound nuclei, in which a strong phonon-nuclear interaction is present. This interaction is normally rotated out with the Foldy–Wouthuysen transformation, but in the presence of strong loss mechanisms this transformation becomes unhelpful. The model that results describes the coupling of vibrational energy to nuclear excitation, but earlier efforts to apply it to the Karabut experiment resulted in inconsistencies. This motivated us to analyze fluctuations due to electron-phonon coupling in metals, which we find here to be a weak effect for Bloch picture phonon exchange, and a somewhat stronger effect with Born–Oppenheimer phonon exchange. As no new physics were found to substantially enhance fractionation, we returned to the basic theory, and carried out a systematic analysis of the three different degrees of freedom that result from simple product approximations for the wavefunction. We find that when there are more virtual phonons than real, a significant enhancement of the coupling strength occurs, corresponding to a new anomalous regime. Conditions on the coupling matrix element and relative state occupation are derived for the anomalous regime, which favors strongly-coupled low energy transitions which constitute a large fraction of all nuclei present. The fractionation power of a sample in the anomalous regime is very much constrained, which allows us to be able to make predictions with the new model. We find that the 30.77 keV transition in 93Nb is likely to be in the anomalous regime in a Nb cathode; that the threshold fractionation energy is too low for excitation of the 30.77 keV transition; but that the threshold fractionation energy is high enough to result in the excitation of the 1565 eV transition in 201Hg, and x-ray emission in the few keV regime consistent with Karabut’s observations.
Excess heat in the Fleischmann–Pons experiment occurs without commensurate energetic nuclear radiation, which motivated us to seek mechanisms capable of fractionating a large quantum, resulting in the lossy spin-boson model. Collimated x-ray emission in the Karabut experiment we interpreted as demonstrating the conversion of vibrational energy to nuclear excitation, as predicted from the lossy spin-boson model; this motivated us to seek physical models that could account for the effect. We found that the coupling strength associated with electron–nuclear and electron–electron coupling was too weak to fractionate keV quanta into 100 MHz vibrations, which motivated us to seek a theory in which nuclear transitions coupled directly to vibrations. These considerations led us to a lattice model with a relativistic description of compound nuclei, in which a strong phonon-nuclear interaction is present. This interaction is normally rotated out with the Foldy–Wouthuysen transformation, but in the presence of strong loss mechanisms this transformation becomes unhelpful. The model that results describes the coupling of vibrational energy to nuclear excitation, but earlier efforts to apply it to the Karabut experiment resulted in inconsistencies. This motivated us to analyze fluctuations due to electron-phonon coupling in metals, which we find here to be a weak effect for Bloch picture phonon exchange, and a somewhat stronger effect with Born–Oppenheimer phonon exchange. As no new physics were found to substantially enhance fractionation, we returned to the basic theory, and carried out a systematic analysis of the three different degrees of freedom that result from simple product approximations for the wavefunction. We find that when there are more virtual phonons than real, a significant enhancement of the coupling strength occurs, corresponding to a new anomalous regime. Conditions on the coupling matrix element and relative state occupation are derived for the anomalous regime, which favors strongly-coupled low energy transitions which constitute a large fraction of all nuclei present. The fractionation power of a sample in the anomalous regime is very much constrained, which allows us to be able to make predictions with the new model. We find that the 30.77 keV transition in 93Nb is likely to be in the anomalous regime in a Nb cathode; that the threshold fractionation energy is too low for excitation of the 30.77 keV transition; but that the threshold fractionation energy is high enough to result in the excitation of the 1565 eV transition in 201Hg, and x-ray emission in the few keV regime consistent with Karabut’s observations.
Optimizing various properties of materials have been under intensive focus for many decades. In recent years, the exposure of ultrafast techniques enhance the possibility of seizing this goal. As by employing these techniques, one can expose the system under strong short fields, and investigate the transient response of various low-lying excitations. Such studies will strengthen our understanding of interplays among various degrees of freedom in correlated materials, and thereby facilitate the chance to manipulate different properties of these systems. Of our particular attention is the electron-lattice dynamics, where modulating a particular vibrational mode of the crystal lattice, will lead to the emergence of new quasi stable'' lattice structures as well as novel transient phenomena. Aside from these experimental prospects, the above mentioned goals were also the subject of an extensive theoretical studies. In this thesis, we investigated the in and out of equilibrium dynamics of electronic systems which are interacting with lattice degrees of freedom. We employed the two-time Keldysh Green's function within the framework of the dynamical mean field theory to conduct our researches on this subject. In our first attempt, we studied the dynamical response of a one-electron system under a linear electron-lattice interaction. We explored the real-time formation of a bound quasiparticle, known as a polaron, under various parameter regimes of the model. We presented that when the carrier is suddenly coupled to the lattice degrees of freedom, the long-time response of the system in the strong coupling limit exhibits both bound, polaronic, and unbound, delocalized, states. We characterized the nature of such a mixed state using the adiabatic picture of the model. We also showed that the formed polaron is dressed by excited phononic states, in contrast to its equilibrium counterpart, where the ground-state phononic states are bounding the electron. We also addressed the response of a many-body electronic system, weakly coupled to a bosonic bath, under various time dependent excitations, which brings the system to a bad-metallic phase. We employed a model which treated the Coulomb repulsive interaction locally. We presented that the relaxation of this excited state varies by the strength of the electron-electron interaction. We demonstrated that, for both insulating and metallic regimes of the system, a slow relaxation dynamics can be observed close to the phase transition from the metallic to insulating regimes of the system. Our analysis revealed that in the metallic side, this slow evolution is rooted in the spin-related physics of the problem. However, in the insulating regimes of the model, our results showed that presence of a gap in the spectral density of the insulating system prohibits the relaxation of the excited particles. We also studied the associated timescale for the adiabatic dynamics near the Mott transition. Our results exhibited that there is a nonadiabatic window'' in the metallic side of the phase transition, in which the adiabatic timescale is extremely long. We pointed out that the presence of such a window is intertwined with the slow relaxation timescale of the spin-related dynamics close to the Mott transition. We also captured an induced metallic phase near metal-to-insulator transition out of equilibrium. We initiated this study using the slave-rotor impurity solver, which is been coupled to the self-energies obtained from the first-order Luttinger-Ward functional for the Phonon degrees of freedom. We presented the emergence of the larger spectral density at small frequencies both in metallic and insulating phases close to the phase transition, which is surrounded by pseudo gaps. We explored the physics of such spectral densities as well as their dependencies on the phononic parameters. We postulated that this response of the system is due to the evolution of the system, in a non-thermal mechanism, towards a temperature which is less than the initial temperature of the system, before coupling to the bath. We also pointed out that the associated very slow relaxation dynamics is the result of the formation of psuedo-gaps around the quasiparticle peak.
We present a dynamical mean-field study of nonperturbative electronic mechanisms, which may lead to significant enhancements of the electron-phonon coupling in correlated electron systems. Analyzing the effects of electronic correlations on the lowest-order electron-phonon processes, we show that in the proximity of the Mott metal-to-insulator transition of the doped square lattice Hubbard model, where the isothermal charge response becomes particularly large at small momenta, the coupling of electrons to the lattice is strongly increased. This, in turn, induces significant corrections to both the electronic self-energy and phonon-mediated pairing interaction, indicating the possible onset of a strong interplay between lattice and electronic degrees of freedom even for small values of the bare electron-phonon coupling.
We develop a generalization of the ghost-rotationally-invariant slave-boson (ghost-RISB) method that incorporates local phonon modes coupled to arbitrary on-site electronic degrees of freedom, enabling a nonperturbative treatment of electron-electron and electron-phonon interactions within an efficient variational framework. The method extends the ghost-orbital construction to capture dynamical self-energy effects and phonon-induced renormalizations beyond static slave-boson approaches. Benchmarking against dynamical mean-field theory (DMFT) results for the Hubbard-Holstein model, we find excellent quantitative agreement for electron quasiparticle weights and phonon properties across a wide range of coupling strengths, and it captures accurately the competition between electron-electron and electron-phonon interactions. We show that the inclusion of the ghost orbitals is crucial to accurately describe the regime of low-frequency, strongly dynamical, phonons. The extended ghost-RISB achieves this accuracy at a fraction of the computational cost of DMFT, due to its self-consistency rooted in static observables instead of dynamical ones, enabling rapid exploration of correlated electron-phonon phase diagrams. We exploit this advantage to characterize the most demanding regime of strong coupling and adiabatic phonons. Our analysis shows a suppression of the superconducting order parameter, which is interpreted as a Franck-Condon-like reduction of the overlap between the phonon wavefunctions associated with empty and doubly-occupied sites in the bipolaronic regime.
Over the last few decades, Born-Oppenheimer (BO) and Born-Oppenheimer-Huang (BOH) treatments for electron-nuclear equation of motion have been considered as the cornerstone for qualitative as well as quantitative exploration and understanding of chemical and physical processes. The BO approximation due to the large mass difference between electrons and nuclei as well as the energy separation among the electronic states could able to predict some of the processes (chemical and physical) satisfactorily at lower energy regime. Such approximation (BO) quite often fails for those cases with the involvement of excited electronic states, in particular, due to the coupling among the states. On the other hand, the BO treatment provides two important quantities, namely, the adiabatic potential energy surfaces (PESs) and the nonadiabatic coupling terms (NACTs) determining the forces, which control the motion of the nuclei in a molecule. The NACTs play a major role in photoexcitation spectra, charge transfer chemical reactions, ferroelectric property and other processes, where significant anomalies are observed between single and multiple PES(s) results. Since the NACTs often exhibit singularity at the close vicinity of degenerate states forming conical intersections (CIs), such coupling terms could break the symmetry of the molecular processes changing the observables qualitatively.
The polaron model is a basic model of quantum field theory describing a single particle interacting with a bosonic field. It arises in many physical contexts. We are mostly concerned with models applicable in the context of an impurity atom in a Bose-Einstein condensate as well as the problem of electrons moving in polar crystals. The model has a simple structure in which the interaction of the particle with the field is given by a term linear in the field’s creation and annihilation operators. In this work, we investigate the properties of this model by providing rigorous estimates on various energies relevant to the problem. The estimates are obtained, for the most part, by suitable operator techniques which constitute the principal mathematical substance of the thesis. The first application of these techniques is to derive the polaron model rigorously from first principles, i.e., from a full microscopic quantum-mechanical many-body problem involving an impurity in an otherwise homogeneous system. We accomplish this for the N + 1 Bose gas in the mean-field regime by showing that a suitable polaron-type Hamiltonian arises at weak interactions as a low-energy effective theory for this problem. In the second part, we investigate rigorously the ground state of the model at fixed momentum and for large values of the coupling constant. Qualitatively, the system is expected to display a transition from the quasi-particle behavior at small momenta, where the dispersion relation is parabolic and the particle moves through the medium dragging along a cloud of phonons, to the radiative behavior at larger momenta where the polaron decelerates and emits free phonons. At the same time, in the strong coupling regime, the bosonic field is expected to behave purely classically. Accordingly, the effective mass of the polaron at strong coupling is conjectured to be asymptotically equal to the one obtained from the semiclassical counterpart of the problem, first studied by Landau and Pekar in the 1940s. For polaron models with regularized form factors and phonon dispersion relations of superfluid type, i.e., bounded below by a linear function of the wavenumbers for all phonon momenta as in the interacting Bose gas, we prove that for a large window of momenta below the radiation threshold, the energy-momentum relation at strong coupling is indeed essentially a parabola with semi-latus rectum equal to the Landau–Pekar effective mass, as expected. For the Fröhlich polaron describing electrons in polar crystals where the dispersion relation is of the optical type and the form factor is formally UV–singular due to the nature of the point charge-dipole interaction, we are able to give the corresponding upper bound. In contrast to the regular case, this requires the inclusion of the quantum fluctuations of the phonon field, which makes the problem considerably more difficult. The results are supplemented by studies on the absolute ground-state energy at strong coupling, a proof of the divergence of the effective mass with the coupling constant for a wide class of polaron models, as well as the discussion of the apparent UV singularity of the Fröhlich model and the application of the techniques used for its removal for the energy estimates.
The properties of the electron-phonon interaction in the presence of a sizable electronic repulsion at finite doping are studied by investigating the metallic phase of the Hubbard-Holstein model with dynamical mean-field theory. Analyzing the quasiparticle weight at finite doping, we find that a large Coulomb repulsion reduces the effect of electron-phonon coupling at low energy, while this reduction is not present at high energy. The renormalization of the electron-phonon coupling induced by the Hubbard repulsion depends in a surprisingly strong and nontrivial way on the phonon frequency. Our results suggest that phonon might affect differently high-energy and low-energy properties and this, together with the effect of phonon dynamics, should be carefully taken into account when the effects of the electron-phonon interaction in a strongly correlated system, like the superconducting cuprates, are discussed.