Exotic Harmonium model: Exploring correlation effects of attractive Coulomb interaction.

Few-body problems involving Coulomb or gravitational interactions between pairs of particles, whether in classical or quantum physics, are generally handled through a standard multipole expansion of the two-body potentials. We discuss an alternative based on a compact, cylindrical Green's function expansion that should have wide applicability throughout physics. Two-electron "direct" and "exchange" integrals in many-electron quantum systems are evaluated to illustrate the procedure which is more compact than the standard one using Wigner coefficients and Slater integrals.

Starting with the three-band extended Hubbard model (or d-p model) widely used to represent the ${\mathrm{CuO}}_{2}$ planes in the high-${\mathit{T}}_{\mathit{c}}$ cuprates, we make a systematic reduction to an effective single-band model using a previously developed cell-perturbation method. The range of parameters for which this mapping is a good approximation is explored in the full Zaanen-Sawatzky-Allen diagram (copper Coulomb repulsion ${\mathit{U}}_{\mathit{d}}$ versus charge-transfer energy \ensuremath{\varepsilon}), together with an investigation of the validity of a further mapping to an effective charge-spin (t-J-V) model. The variation of the effective single-band parameters with the parameters of the underlying multi-band model is investigated in detail, and the parameter regime where the model represents the high-${\mathit{T}}_{\mathit{c}}$ cuprates is examined for specific features that might distinguish it from the general case. In particular, we consider the effect of Coulomb repulsions on oxygen (${\mathit{U}}_{\mathit{p}}$) and between copper and oxygen (${\mathit{V}}_{\mathit{pd}}$). We find that the reduction to an effective single-band model is generally valid for describing the low-energy physics, and that ${\mathit{V}}_{\mathit{pd}}$ and ${\mathit{U}}_{\mathit{p}}$ (unless unrealistically large) actually slightly improve the convergence of the cell-perturbation method. Unlike in the usual single-band Hubbard model, the effective intercell hopping and Coulomb interactions are different for electrons and holes.We find that this asymmetry, which vanishes in the extreme Mott-Hubbard regime (${\mathit{U}}_{\mathit{d}}$\ensuremath{\ll}\ensuremath{\varepsilon}), is quite appreciable in the charge-transfer regime (${\mathit{U}}_{\mathit{d}}$\ensuremath{\gtrsim}\ensuremath{\varepsilon}), particularly for the effective Coulomb interactions. We show that for doped holes (forming Zhang-Rice singlets) on neighboring cells the interaction induced by ${\mathit{V}}_{\mathit{pd}}$ can even be attractive due to locally enhanced pd hybridization, while this cannot occur for electrons. The Coulomb interaction induced by ${\mathit{U}}_{\mathit{p}}$ is always repulsive; in addition ${\mathit{U}}_{\mathit{p}}$ gives rise to a ferromagnetic spin-spin interaction which opposes antiferromagnetic superexchange. We show that for hole-doped systems this leads to a subtle cancellation of attractive and repulsive contributions, due to antiferromagnetic and charge-polarization effects, to the net static interaction in a charge-spin (t-J-V) model, and we discuss the significance of this result. The asymmetry in the ee, hh, and eh effective hopping parameters can be particularly large for next-nearest neighbors. Specializing to cuprate parameters, we find that the asymmetry in the nearest-neighbor hopping parameters almost vanishes (accidentally), while the next-nearest-neighbor hopping parameter ${\mathit{t}}^{\ensuremath{'}}$ is close to zero for electrons but is appreciable for holes (${\mathit{t}}^{\ensuremath{'}}$\ensuremath{\approxeq}-0.06 eV). The effective Coulomb interaction between doped holes is found to be repulsive, and even slightly larger than for electrons. All the underlying d-p parameters make significant contributions to the effective interactions and it is shown that certain approximations, such as ${\mathit{U}}_{\mathit{d}}$=\ensuremath{\infty} and ${\mathit{t}}_{\mathit{pp}}$=0, can be qualitatively incorrect. \textcopyright{} 1996 The American Physical Society.

A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g., MD, integral equations, DFT) to describe quantum systems. The classical system has an effective temperature, local chemical potential, and pair interaction that are defined by requiring equivalence of the grand potential and its functional derivatives with respect to the external and pair potentials for the classical and quantum systems. Practical inversion of this mapping for the classical properties is effected via the hypernetted chain approximation, leading to representations as functionals of the quantum pair correlation function. As an illustration, the parameters of the classical system are determined approximately such that ideal gas and weak coupling RPA limits are preserved (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper, we consider the variable-coefficient power-law nonlinear Schrödinger equations (NLSEs) with external potential as well as the gain or loss function. First, we generalize the similarity transformation method, which converts the variable coefficient NLSE with two power-law nonlinear terms to the autonomous dual-power NLS equation with constant coefficients. Then, we obtain the exact solutions of the variable-coefficient NLSE. Moreover, we discuss the solitary-wave solutions for equations with vanishing potential, space-quadratic potential and optical lattice potential, which are applied to many branches of physics.

Ergodicity of quantum dynamics is often defined through statistical properties of energy eigenstates, as exemplified by Berry's conjecture in single-particle quantum chaos and the eigenstate thermalization hypothesis in many-body settings. In this work, we investigate whether quantum systems can exhibit a stronger form of ergodicity, wherein any time-evolved state uniformly visits the entire Hilbert space over time. We call such a phenomenon complete Hilbert-space ergodicity (CHSE), which is more akin to the intuitive notion of ergodicity as an inherently dynamical concept. CHSE cannot hold for time-independent or even time-periodic Hamiltonian dynamics, owing to the existence of (quasi)energy eigenstates which precludes exploration of the full Hilbert space. However, we find that there exists a family of aperiodic, yet deterministic drives with minimal symbolic complexity-generated by the Fibonacci word and its generalizations-for which CHSE can be proven to occur. Our results provide a basis for understanding thermalization in general time-dependent quantum systems.

We show that the electron correlation of a molecular system can be enhanced or diminished through the application of a homogeneous electric field antiparallel or parallel to the system's intrinsic dipole moment. More generally, we prove that any external stimulus that significantly changes the expectation value of a one-electron operator with nondegenerate minimum and maximum eigenvalues can be used to control the degree of a molecule's electron correlation. Computationally, the effect is demonstrated in ${\mathrm{HeH}}^{+}, {\mathrm{MgH}}^{+}$, BH, HCN, ${\mathrm{H}}_{2}\mathrm{O}$, HF, formaldehyde, and a fluorescent dye. Furthermore, we show in calculations with an array of formaldehyde (${\mathrm{CH}}_{2}\mathrm{O}$) molecules that the field can control not only the electron correlation of a single formaldehyde molecule but also the entanglement among formaldehyde molecules. The quantum control of correlation and entanglement has potential applications in the design of molecules with tunable properties and the stabilization of qubits in quantum computations.

It is customary to couple a quantum system to external classical fields. One application is to couple the global symmetries of the system (including the Poincaré symmetry) to background gauge fields (and a metric for the Poincaré symmetry). Failure of gauge invariance of the partition function under gauge transformations of these fields reflects ’t Hooft anomalies. It is also common to view the ordinary (scalar) coupling constants as background fields, i.e. to study the theory when they are spacetime dependent. We will show that the notion of ’t Hooft anomalies can be extended naturally to include these scalar background fields. Just as ordinary ’t Hooft anomalies allow us to deduce dynamical consequences about the phases of the theory and its defects, the same is true for these generalized ’t Hooft anomalies. Specifically, since the coupling constants vary, we can learn that certain phase transitions must be present. We will demonstrate these anomalies and their applications in simple pedagogical examples in one dimension (quantum mechanics) and in some two, three, and four-dimensional quantum field theories. An anomaly is an example of an invertible field theory, which can be described as an object in (generalized) differential cohomology. We give an introduction to this perspective. Also, we use Quillen’s superconnections to derive the anomaly for a free spinor field with variable mass. In a companion paper we will study four-dimensional gauge theories showing how our view unifies and extends many recently obtained results.

Echoes are ubiquitous phenomena in several branches of physics, ranging from acoustics, optics, condensed matter and cold atoms to geophysics. They are at the base of a number of very useful experimental techniques, such as nuclear magnetic resonance, photon echo and time-reversal mirrors. Particularly interesting physical effects are obtained when the echo studies are performed on complex systems, either classically chaotic, disordered or many-body. Consequently, the term Loschmidt echo has been coined to designate and quantify the revival occurring when an imperfect time-reversal procedure is applied to a complex quantum system, or equivalently to characterize the stability of quantum evolution in the presence of perturbations. Here, we present the articles which discuss the work that has shaped the field in the past few years.

Simulation of Coulomb interaction effects in electron sources

Ultracold quantum gases provide a unique setting for studying and understanding the properties of interacting quantum systems. Here, we investigate a multi-component system of 87Rb–39K Bose–Einstein condensates (BECs) with tunable interactions both theoretically and experimentally. Such multi-component systems can be characterized by their miscibility, where miscible components lead to a mixed ground state and immiscible components form a phase-separated state. Here we perform the first full simulation of the dynamical expansion of this system including both BECs and thermal clouds, which allows for a detailed comparison with experimental results. In particular we show that striking features emerge in time-of-flight (TOF) for BECs with strong interspecies repulsion, even for systems which were separated in situ by a large gravitational sag. An analysis of the centre of mass positions of the BECs after expansion yields qualitative agreement with the homogeneous criterion for phase-separation, but reveals no clear transition point between the mixed and the separated phases. Instead one can identify a transition region, for which the presence of a gravitational sag is found to be advantageous. Moreover, we analyse the situation where only one component is condensed and show that the density distribution of the thermal component also shows some distinct features. Our work sheds new light on the analysis of multi-component systems after TOF and will guide future experiments on the detection of miscibility in these systems.

Densities, density-functionals and electron fluids

An approach for obtaining the ground state of Coulombic many-body systems is presented. This approach is based on the path-integral renormalization-group method with nonorthogonal Slater determinants, is free of the negative sign problem, and can handle higher dimensional systems with consideration of the correlation effect. Furthermore, it can be easily extended to the multicomponent quantum systems that contain more than two kinds of quantum particles. According to our results obtained with the present approach, it achieves the same accuracy as the variational Monte Carlo method with a few Slater determinants and enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation.

Self-powered photoelectrochemical immunosensor with triple enhanced photoelectric response for sensitive detection of cTnI

Differential equation for the ground-state density of a model spin-compensated atom in an external potential

For a general many-electron system, we demonstrate that the Luttinger theorem is obeyed if the electron excitation spectrum is gapless, no matter whether it shows the Landau Fermi liquid or non-Fermi-liquid behavior. Furthermore, we give a general expression of the nonlinear response of the system to external potentials, and apply it for external gauge fields and an on-site time-dependent external potential, where the latter problem can be exactly solved.