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We have considered a system consisting of two coupled quantum dots containing two electrons, i.e., two quantum dots next to each other with one excess electron each, subjected to an uniform magnetic field perpendicular to the quantum dots plane. The effect of different confinement potential profiles under which the electrons are subjected is studied. This study has been performed in the light of interest in fundamental logical quantum-gate operations: we have been concerned in analysing the behaviour of the main physical quantities which should be involved in a two-qubit quantum-gate operation for two different profiles of confinement found in literature. Our purpose was to establish how sensitive the physical quantities are to the confinement profile and in which range of magnetic field this issue can be critical., Comment: 10 pages, 7 figures

We compute deviations from ideal gas behavior of the pressure, density, and Bose-Einstein condensation temperature of a relativistic gas of charged scalar bosons caused by the current-current interaction induced by electromagnetic quantum fluctuations treated via scalar quantum electrodynamics. We obtain expressions for those quantities in the ultra-relativistic and nonrelativistic limits, and present numerical results for the relativistic case., Comment: 5 pages, 5 figures

We investigate the dispersion of a classical electromagnetic field in a relativistic ideal gas of charged bosons using scalar quantum electrodynamics at finite temperature and charge density. We derive the effective electromagnetic responses and the electromagnetic propagation modes that characterize the gas as a left-handed material with negative effective index of refraction $n_{\rm eff}=-1$ below the transverse plasmon frequency. In the condensed phase, we show that the longitudinal plasmon dispersion relation exhibits a roton-type local minimum that disappears at the transition temperature., Comment: 6 pages, 5 figures

We show that a gas of relativistic electrons is a left-handed material at low frequencies by computing the effective electric permittivity and effective magnetic permeability that appear in Maxwell's equations in terms of the responses appearing in the constitutive relations, and showing that the former are both negative below the {\it same} frequency, which coincides with the zero-momentum frequency of longitudinal plasmons. We also show, by explicit computation, that the photonic mode of the electromagnetic radiation does not dissipate energy, confirming that it propagates in the gas with the speed of light in vacuum, and that the medium is transparent to it. We then combine those results to show that the gas has a negative effective index of refraction $n_{\rm eff}=-1$. We illustrate the consequences of this fact for Snell's law, and for the reflection and transmission coefficients of the gas., Comment: 8 pages, 3 figures

We study the system consisted of two electrons in a quantum dot with a three-dimensional harmonic confinement potential under the effect of a magnetic field. Specifically, two different confinement conditions are considered, one isotropic three-dimensional and the other anisotropic quasi-two-dimensional. Singlet and triplet lowest states properties as the energy, the exchange coupling, the two-electron density function and the spatial spreading of the two electrons in terms of the variance along the x-direction are analysed. In this study we employ the full configuration interaction method with Cartesian anisotropic Gaussian-type orbitals as basis set. These functions allow to explore the confining characteristics of a potential due to their flexibility of using different exponents for each direction in space. The convergence of the results, depending on the size of the set of basic functions, is examined and the oscillations of different physical quantities, concerning the singlet and triplet states, as a function of the magnetic field are discussed., Comment: 8 pages, 4 figures

We have studied a system consisted of two coupled quantum dots containing two electrons subjected by a laser field. The effect of the laser is described by the dressed-band approach involving the concept of the conduction/valence effective mass, valid far from resonance. The interaction between the electrons and the quantum dots is described by a phenomenological tridimensional potential, which simulates quantum dots in GaAs heterostructure. In this study we have employed the approach already presented in a previous work [Olavo et al., J. Phys. B: At. Mol. Opt. Phys. {\bf 49}, 145004 (2016)]. We have used a code based on the full interaction configuration method. We have employed as basis set the {\it Cartesian anisotropic Gaussian-type} orbitals which allows one to explore the confining characteristics of a potential due to their flexibility of using different exponents for each direction space. We present an analysis based on the energy levels of the singlet and triplet as function of the confinement parameters.

We show that two-particle interferences can be used to probe the nuclear motion in a doubly-excited hydrogen molecule. The dissociation of molecular hydrogen by electron impact involves several decay channels, associated to different molecular rotational states, which produce quantum interferences in the detection of the atomic fragments. Thanks to the correlations between the angular momentum and vibrational states of the molecule, the fragments arising from each dissociation channel carry out a phase-shift which is a signature of the molecule rotation. These phase-shifts, which cannot be observed in a single-atom detection scheme, may be witnessed in realistic experimental conditions in a time-of-flight coincidence measurement. We analyse the interferences arising from the two lowest-energy rotational states of a para-hydrogen molecule. Our result shows the relevance of two-fragments correlations to track the molecular rotation., Comment: 5 pages, 3 Figures. Submitted

We describe electromagnetic propagation in a relativistic electron gas at finite temperatures and carrier densities. Using quantum electrodynamics at finite temperatures, we obtain electric and magnetic responses and general constitutive relations. Rewriting the propagator for the electromagnetic field in terms of the electric and magnetic responses, we identify the modes that propagate in the gas. As expected, we obtain the usual collective excitations, i.e., a longitudinal electric and two transverse magnetic plasmonic modes. In addition, we find a purely photonic mode that satisfies the wave equation in vacuum, for which the electron gas is transparent. We present dispersion relations for the plasmon modes at zero and finite temperatures and identify the intervals of frequency and wavelength where both electric and magnetic responses are simultaneously negative, a behavior previously thought not to occur in natural systems.

We compute the real and imaginary parts of the electric permittivities and magnetic permeabilities for relativistic electrons from quantum electrodynamics at finite temperature and density. A semiclassical approximation establishes the conditions for neglecting nonlinear terms in the external electromagnetic fields as well as electron-electron interactions. We obtain both the electric and magnetic responses in a unified manner and relate them to longitudinal and transverse collective plasma oscillations. We demonstrate that such collective modes are thresholds for a metamaterial regime of the electron plasma which exhibits simultaneously negative longitudinal permittities and permeabilities. For nonzero temperatures, we obtain electromagnetic responses given by one-dimensional integrals to be numerically calculated, whereas for zero temperature we find analytic expressions for both their real/dispersive and imaginary/absorptive parts., Comment: 11 pages, 3 figures

We investigate the electromagnetic response of a relativistic Fermi gas at finite temperatures. Our theoretical results are first-order in the fine-structure constant. The electromagnetic permittivity and permeability are introduced via general constitutive relations in reciprocal space, and computed for different values of the gas density and temperature. As expected, the electric permittivity of the relativistic Fermi gas is found in good agreement with the Lindhard dielectric function in the low-temperature limit. Applications to condensed-matter physics are briefly discussed. In particular, theoretical results are in good agreement with experimental measurements of the plasmon energy in graphite and tin oxide, as functions of both the temperature and wave vector. We stress that the present electromagnetic response of a relativistic Fermi gas at finite temperatures could be of potential interest in future plasmonic and photonic investigations.

The electric permittivities and magnetic permeabilities for a relativistic electron gas are calculated from quantum electrodynamics at finite temperature and density as functions of temperature, chemical potential, frequency, and wavevector. The polarization and the magnetization depend linearly on both electric and magnetic fields, and are the sum of a zero-temperature and zero-density vacuum part with a temperature- and chemical potential-dependent medium part. Analytic calculations lead to generalized expressions that depend on three scalar functions. In the nonrelativistic limit, results reproduce the Lindhard formula. In the relativistic case, and in the long wavelength limit, we obtain: i) for $\omega=0$, generalized susceptibilities that reduce to known nonrelativistic limits; ii) for $\omega \neq 0$, Drude-type responses at zero and at high temperatures. The latter implies that one may have both $\epsilon$ and $\mu$ simultaneously negative, a behavior characteristic of metamaterials. This unambiguously indicates that the relativistic electron plasma is one of nature's candidates for the realization of a negative index of refraction system. Moreover, Maxwell's equations in the medium yield the dispersion relation and the index of refraction of the electron plasma. Present results should be relevant for plasma physics, astrophysical observations, synchrotrons, and other environments with fast moving electrons., Comment: Submitted to PRD

We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the inverted potential, the usual quadratic approximation fails due to the existence of multiple classical solutions and caustics. Using the tools of catastrophe theory, we identify the relevant classical solutions, showing that at most two have to be considered. This corresponds to the first step towards the study of spontaneous symmetry breaking and thermal phase transitions in the non-perturbative framework of the boundary effective theory., Comment: 10 pages, 11 figures

We calculate the one-loop effective potential at finite temperature for a system of massless scalar fields with quartic interaction $\lambda\phi^4$ in the framework of the boundary effective theory (BET) formalism. The calculation relies on the solution of the classical equation of motion for the field, and Gaussian fluctuations around it. Our result is non-perturbative and differs from the standard one-loop effective potential for field values larger than $T/\sqrt{\lambda}$., Comment: 10 pages, 3 figures

We use the boundary effective theory (BET) approach to thermal field theory in order to calculate the pressure of a system of massless scalar fields with quartic interaction. The method naturally separates the infrared physics, and is essentially non-perturbative. To lowest order, the main ingredient is the solution of the free Euler-Lagrange equation with non-trivial (time) boundary conditions. We derive a resummed pressure, which is in good agreement with recent calculations found in the literature, following a very direct and compact procedure., Comment: 10 pages, 4 figures

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field $\phi_c$, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schr\"{o}dinger field-representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle-point for fixed boundary fields, which is the classical field $\phi_c$, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally-reduced effective theory for the thermal system. We calculate the two-point correlation as an example., Comment: 13 pages, 1 figure

Galileo, in the XVII century, observed that the small oscillations of a pendulum seem to have constant period. In fact, the Taylor expansion of the period map of the pendulum is constant up to second order in the initial angular velocity around the stable equilibrium. It is well known that, for small oscillations of the pendulum and small intervals of time, the dynamics of the pendulum can be approximated by the dynamics of the harmonic oscillator. We study the dynamics of a family of mechanical systems that includes the pendulum at small neighbourhoods of the equilibrium but after long intervals of time so that the second order term of the period map can no longer be neglected. We analyze such dynamical behaviour through a renormalization scheme acting on the dynamics of this family of mechanical systems. The main theorem states that the asymptotic limit of this renormalization scheme is universal: it is the same for all the elements in the considered class of mechanical systems. As a consequence, we obtain an universal asymptotic focal decomposition for this family of mechanical systems. This paper is intended to be the first of a series of articles aiming at a semiclassical quantization of systems of the pendulum type as a natural application of the focal decomposition associated to the two-point boundary value problem., Comment: 31 pages, 3 figures

We analyze one-dimensional photonic superlattices which alternate layers of air and a left-handed material. We assume Drude-type dispersive responses for the dielectric permittivity and magnetic permeability of the left-handed material. Maxwell's equations and the transfer-matrix technique are used to derive the dispersion relation for the propagation of obliquely incident optical fields. The photonic dispersion indicates that the growth-direction component of the electric (or magnetic) field leads to the propagation of electric (or magnetic) plasmon polaritons, for either TE or TM configurations. Furthermore, we show that if the plasma frequency is chosen within the photonic $=0$ zeroth-order bandgap, the coupling of light with plasmons weakens considerably. As light propagation is forbidden in that particular frequency region, the plasmon-polariton mode reduces to a pure plasmon mode., Comment: 4 pages, 4 figures

We present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. We identify the stochastic variable of the effective statistical theory that we derive as a boundary configuration and a zero mode relevant to the discussion of infrared physics. We illustrate our formulation by computing the partition function of an interacting one-dimensional quantum mechanical system at finite temperature from the path-integral representation for the density matrix. The method of calculation provides an alternative to the usual sum over periodic trajectories: it sums over paths with coincident endpoints, and includes non-vanishing boundary terms. An appropriately modified expansion into Matsubara modes provides a natural separation of the zero-mode physics. This feature may be useful in the treatment of infrared divergences that plague the perturbative approach in thermal field theory., Comment: 9 pages, 5 figures

Several relevant aspects of quantum-field processes can be well described by semiclassical methods. In particular, the knowledge of non-trivial classical solutions of the field equations, and the thermal and quantum fluctuations around them, provide non-perturbative information about the theory. In this work, we discuss the calculation of the one-loop effective action from the semiclasssical viewpoint. We intend to use this formalism to obtain an accurate expression for the decay rate of non-static metastable states., Comment: 4 pages, 1 figure. To appear in the proceedings of Strong and Electroweak Matter (SEWM08), Amsterdam

We obtain the primitively divergent diagrams in $\kappa$-deformed scalar field in four-dimensional spacetime with quartic self-interaction in order to investigate the effect of the fundamental length $q=1/(2\kappa)$ on such diagrams. Thanks to $\kappa$-deformation, we find that the dimensionally regularized forms of the diagrams lead to finite results in the limit of space-time dimension four. The effect of the deformation appears as a displacement of the poles in the complex plane.

We present a systematic semiclassical procedure to compute the partition function for scalar field theories at finite temperature. The central objects in our scheme are the solutions of the classical equations of motion in imaginary time, with spatially independent boundary conditions. Field fluctuations -- both field deviations around these classical solutions, and fluctuations of the boundary value of the fields -- are resummed in a Gaussian approximation. In our final expression for the partition function, this resummation is reduced to solving certain ordinary differential equations. Moreover, we show that it is renormalizable with the usual 1-loop counterterms., Comment: 24 pages, 5 postscript figures

We describe the Feynman rules for the construction of the Dimensionally Reduced Action (DRA) for a phi^4 field theory, as well as rules for the construction of the connected Green functions and the Dimensionally Reduced Effective Action (DREA), the effective action obtained from the DRA. Two and four-point connected Green functions are calculated to illustrate the application of those rules, and to exhibit the subtraction of UV divergences. As the DRA formalism expands about a background field, instead of the high temperature expansion obtained in the usual dimensional reduced field theory, we derive an expansion that is defined for all range of temperatures. We make a low temperature analysis of the DREA by considering soft modes. In particular, we study the case of near zero mass., Comment: 10 pages, 10 figures

We compute one-loop correlation functions for the fluctuations of an interface using a field theory model. We obtain them from Feynman diagrams drawn with a propagator which is the inverse of the Hamiltonian of a Poschl-Teller problem. We derive an expression for the propagator in terms of elementary functions, show that it corresponds to the usual spectral sum, and use it to calculate quantities such as the surface tension and interface profile in two and three spatial dimensions. The three-dimensional quantities are rederived in a simple, unified manner, whereas those in two dimensions extend the existing literature, and are applicable to thin films. In addition, we compute the one-loop self-energy, which may be extracted from experiment, or from Monte Carlo simulations. Our results may be applied in various scenarios, which include fluctuations around topological defects in cosmology, supersymmetric domain walls, Z(N) bubbles in QCD, domain walls in magnetic systems, interfaces separating Bose-Einstein condensates, and interfaces in binary liquid mixtures., Comment: RevTeX, 13 pages, 6 figures

We derive and analyze the perturbation series for the classical effective action in quantum statistical mechanics, treated as a toy model for the dimensionally reduced effective action in quantum field theory at finite temperature. The first few terms of the series are computed for the harmonic oscillator and the quartic potential., Comment: 7 pages. Published in the Proceedings of the XXIII Brazilian National Meeting on Particles and Fields (October 15-19, Aguas de Lindoia, SP, Brazil), http://www.sbf1.if.usp.br/eventos/enfpc/xxiii/procs/RES191.pdf Eqs.(21) and (23) corrected

We present a simple method to deal with caustics in the semiclassical approximation to the thermal density matrix of a particle moving on the line. For simplicity, only its diagonal elements are considered. The only ingredient we require is the knowledge of the extrema of the Euclidean action. The procedure makes use of complex trajectories, and is applied to the quartic double-well potential., Comment: 20 pages, 7 figures. Revised version, accepted for publication in Phys. Rev. E

We give graphical rules, based on earlier work for the functional Schrodinger equation, for constructing the density matrix for scalar and gauge fields at finite temperature T. More useful is a dimensionally-reduced effective action (DREA) constructed from the density matrix by further functional integration over the arguments of the density matrix coupled to a source. The DREA is an effective action in one less dimension which may be computed order by order in perturbation theory or by dressed-loop expansions; it encodes all thermal matrix elements. The DREA is useful because it gives a dimensionally-reduced field theory usable at any T including infinity, where it yields the usual dimensionally-reduced field theory (DRFT). However, it cannot and does not have spurious infinities which sometimes occur in the density matrix or the DRFT; these come from ln T factors at infinite temperature. An example of spurious divergences in the DRFT occurs in d 2+1 $\phi^4$ theory dimensionally reduced to d=2. We show that the rules for the DREA replace these "wrong" divergences in physical parameters by calculable powers of ln T; we also compute the phase transition temperature of this theory at one loop order., Comment: 23 pages, LaTeX, no figures

We present a simple method to deal with caustics in the semiclassical approximation to the partition function of a one-dimensional quantum system. The procedure, which makes use of complex trajectories, is applied to the quartic double-well potential., Comment: 5 pages, 1 figure, Latex. Contribution to the Proceedings of the XXI Brazilian National Meeting on Particles and Fields (Sao Lourenco, October 23-27, 2000)

We use a path integral formalism to derive the semiclassical series for the partition function of a particle in D dimensions. We analyze in particular the case of attractive central potentials, obtaining explicit expressions for the fluctuation determinant and for the semiclassical two-point function in the special cases of the harmonic and single-well quartic anharmonic oscillators. The specific heat of the latter is compared to precise WKB estimates. We conclude by discussing the possible extension of our results to field theories., Comment: REVTEX,14 pages, 2 figures, final version to appear in Phys. Rev. E

We study the viscosity corrections to the growth rate of nucleating bubbles in a first order phase transition in scalar field theory. We obtain the non-equilibrium equation of motion of the coordinate that describes small departures from the critical bubble and extract the growth rate consistently in weak coupling and in the thin wall limit. Viscosity effects arise from the interaction of this coordinate with the stable quantum and thermal fluctuations around a critical bubble. In the case of 1+1 dimensions we provide an estimate for the growth rate that depends on the details of the free energy functional. In 3+1 dimensions we recognize robust features that are a direct consequence of the thin wall approximation and give the leading viscosity corrections.These are long-wavelength hydrodynamic fluctuations that describe surface waves, quasi-Goldstone modes which are related to ripples on interfaces in phase ordered Ising-like systems. We discuss the applicability of our results to describe the growth rate of hadron bubbles in a quark-hadron first order transition., Comment: 40 pages, 4 figures, revtex, minor changes, to be published in Phys. Rev. D

We derive the semiclassical series for the partition function in Quantum Statistical Mechanics (QSM) from its path integral representation. Each term of the series is obtained explicitly from the (real) minima of the classical action. The method yields a simple derivation of the exact result for the harmonic oscillator, and an accurate estimate of ground-state energy and specific heat for a single-well quartic anharmonic oscillator. As QSM can be regarded as finite temperature field theory at a point, we make use of Feynman diagrams to illustrate the non-perturbative character of the series: it contains all powers of $\hbar$ and graphs with any number of loops; the usual perturbative series corresponds to a subset of the diagrams of the semiclassical series. We comment on the application of our results to other potentials, to correlation functions and to field theories in higher dimensions., Comment: 18 pages, 4 figures. References updated

We derive the semiclassical series for the partition function of a one-dimensional quantum-mechanical system consisting of a particle in a single-well potential. We do this by applying the method of steepest descent to the path-integral representation of the partition function, and we present a systematic procedure to generate the terms of the series using the minima of the Euclidean action as the only input. For the particular case of a quartic anharmonic oscillator, we compute the first two terms of the series, and investigate their high and low temperature limits. We also exhibit the nonperturbative character of the terms, as each corresponds to sums over infinite subsets of perturbative graphs. We illustrate the power of such resummations by extracting from the first term an accurate nonperturbative estimate of the ground-state energy of the system and a curve for the specific heat. We conclude by pointing out possible extensions of our results which include field theories with spherically symmetric classical solutions., Comment: 25 pages + 5 figures

We study a spin-1/2 charged particle with gyromagnetic factor g>2 moving in a plane threaded by a magnetic flux tube. We prove that, if the magnetic field (i) has radial symmetry, (ii) has compact support and (iii) does not change sign, there is at least one bound state for each angular momentum l in the interval [0,v], where v (assumed positive) is the total magnetic flux in units of the quantum of flux., Comment: 4 pages, REVTEX. Final version, to appear in J. Phys. A: Math. Gen

We study a relativistic two-dimensional electron gas in the presence of a uniform external magnetic field and a random static scalar potential. We compute, in first order perturbation theory, the averages of the charge density and of the transverse conductivity for a white-noise potential, and show that, within this treatment, their quantized values are modified by the disorder., Comment: ReVTeX, 7 pages, 1 ps figure. To appear in Mod. Phys. Lett. B. The last reference was corrected

We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on Catastrophe Theory to analyze the pattern of extrema of the corresponding path-integral. We exhibit the propagator in the background of the different extrema and use it to compute the fluctuation determinant and to develop a (nonperturbative) semiclassical expansion which allows for the calculation of correlation functions. We discuss the examples of the single and double-well quartic anharmonic oscillators, and the implications of our results for higher dimensions., Comment: Invited talk at the La Plata meeting on `Trends in Theoretical Physics', La Plata, April, 1997; 14 pages + 5 ps figures. Some cosmetical modifications, and addition of some references which were missing in the previous version

We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the potential. For high temperatures, the semiclassical expression is dominated by single closed paths. As we lower the temperature, new closed paths may appear, including tunneling paths. The transition from single to multiple-path regime corresponds to well-defined catastrophes. Tunneling sets in whenever they occur. Our formula fully accounts for this feature., Comment: 5 figures, revtex file

We examine Gamow's method for calculating the decay rate of a wave function initially located within a potential well. Using elementary techniques, we examine a very simple, exactly solvable model, in order to show why it is so reliable for calculating decay rates, in spite of its conceptual problems. We also discuss the regime of validity of the exponential decay law., Comment: 10 pages, 1 figure, REVTEX. A few modifications, references updated

We study the problem of an electron in two dimensions in the presence of a magnetic vortex with a step-like profile. Dependending on the values of the effective mass and gyromagnetic factor of the electron, it may be trapped by the vortex. The bound state spectrum is obtained numerically, and some limiting cases are treated analytically., Comment: 8 pages, latex, 4 figures

The density of states and the Hall conductivity of a two-dimensional electron gas in a uniform magnetic field and in the presence of a delta impurity are exactly calculated using elementary field theoretic techniques. Although these results are not new, our treatment is explicitly gauge-invariant, and can be easily adapted to other problems involving a delta potential., Comment: 12+1 pages, 1 ps figure, REVTEX. Corrigendum added

We study a relativistic two-dimensional free electron gas in the presence of a uniform external magnetic field and a random static scalar potential. We compute the expectation values of the charge density and the conductivity tensor, averaged over the random potential in first order perturbation theory. We discuss the effect of a zero vs. finite range correlation length of the random potential., Comment: 9 pages, 4 figures, REVTEX. Last paragraph of section IV removed, references updated