Flat Density Of States Research Articles

Penrose tilings as jammed solids.

Penrose tilings form lattices, exhibiting fivefold symmetry and isotropic elasticity, with inhomogeneous coordination much like that of the force networks in jammed systems. Under periodic boundary conditions, their average coordination is exactly four. We study the elastic and vibrational properties of rational approximants to these lattices as a function of unit-cell size N(S) and find that they have of order sqrt[N(S)] zero modes and states of self-stress and yet all their elastic moduli vanish. In their generic form, obtained by randomizing site positions, their elastic and vibrational properties are similar to those of particulate systems at jamming with a nonzero bulk modulus, vanishing shear modulus, and a flat density of states.

Saturation of two-level systems and charge noise in Josephson junction qubits

We study the charge noise ${S}_{Q}$ in Josephson qubits produced by fluctuating two-level systems (TLSs) with electric-dipole moments in the substrate. The TLSs are driven by an alternating electric field of angular frequency $\ensuremath{\Omega}$ and electric field intensity $I$. It is not widely appreciated that TLS in small qubits can easily be strongly saturated if $I⪢{I}_{c}$, where ${I}_{c}$ is the critical electric field intensity. To investigate the effect of saturation on the charge noise, we express the noise spectral density in terms of density-matrix elements. To determine the dependence of the density-matrix elements on the ratio $I/{I}_{c}$, we find the steady-state solution for the density matrix using the Bloch-Redfield differential equations. We then obtain an expression for the spectral density of charge fluctuations as a function of frequency $f$ and the ratio $I/{I}_{c}$. We find $1/f$ charge noise at low frequencies, and that the charge noise is white (constant) at high frequencies. Using a flat density of states, we find that TLS saturation has no effect on the charge noise at either high or low frequencies.

A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics

We study a generic problem of dissipative quantum mechanics, a small local quantum system with discrete states coupled in an arbitrary way (i.e. not necessarily linear) to several infinitely large particle or heat reservoirs. For both bosonic or fermionic reservoirs we develop a quantum field-theoretical diagrammatic formulation in Liouville space by expanding systematically in the reservoir-system coupling and integrating out the reservoir degrees of freedom. As a result we obtain a kinetic equation for the reduced density matrix of the quantum system. Based on this formalism, we present a formally exact perturbative renormalization group (RG) method from which the kernel of this kinetic equation can be calculated. It is demonstrated how the nonequilibrium stationary state (induced by several reservoirs kept at different chemical potentials or temperatures), arbitrary observables such as the transport current, and the time evolution into the stationary state can be calculated. Most importantly, we show how RG equations for the relaxation and dephasing rates can be derived and how they cut off generically the RG flow of the vertices. The method is based on a previously derived real-time RG technique [1-4] but formulated here in Laplace space and generalized to arbitrary reservoir-system couplings. Furthermore, for fermionic reservoirs with flat density of states, we make use of a recently introduced cutoff scheme on the imaginary frequency axis [5] which has several technical advantages. Besides the formal set-up of the RG equations for generic problems of dissipative quantum mechanics, we demonstrate the method by applying it to the nonequilibrium isotropic Kondo model. We present a systematic way to solve the RG equations analytically in the weak-coupling limit and provide an outlook of the applicability to the strong-coupling case.

Universality in Voltage-driven Nonequilibrium Phase Transitions

We consider the non-equilibrium ferromagnetic transition of a mesoscopic sample of a resistive Stoner ferromagnet coupled to two paramagnetic leads. The transition is controlled by either the lead temperature T or the transport voltage V applied between the leads. We calculate the T and V dependence of the magnetization. For systems with a flat density of states we find within mean-field theory that even at finite bias the magnetization does not depend on the position along the sample axis, although the charge density and other quantities do vary. This may be relevant for possible spintronics applications. In addition, we establish a generalized control parameter in terms of T and V which allows for a universal description of the temperature- and voltage-driven transition.

Generation- Recombination Noise in Amorphous Semiconductors

ABSTRACTWe examine different approaches to the analysis of noise in amorphous hydrogenated silicon associated with trapping and generation – recombination processes, which appear to predict very different noise spectra. In one approach the broad noise spectrum observed is assumed to be composed of a distribution of Lorentzian noise spectra, each associated with traps at a given energy depth, with appropriate weighting according to the energy distribution of characteristic time constants. This latter weighting is taken to mirror the energy distribution of states in the gap. This represents a linear superposition of the (weighted) contribution from individual trapping levels, each with its own characteristic time constant. This approach thus assumes that each trap level is an independent source of fluctuation in free carrier number, unaffected by the presence of other traps in the material. At first sight this assertion seems plausible, since in the multi-trapping situation envisaged, cross-correlation effects must be very small. However, the presence of several groups of traps, or, in the limit, a continuum, results in a distribution of characteristic time constants, which is not a simple linear superposition of the time constants for each level. Thus the assertion that a flat density of states, or a region which is flat, such as the top of a broadened level, results in a region of 1/f slope in the noise spectrum, may not be valid. We present an alternative model in which the distribution of time constants is appropriately incorporated, and compare the predictions of this model with the ‘superposition’ approach, using computed noise spectra.

Slave-boson calculation of the Landau parameters of the one-band Hubbard model

We present a microscopic slave-boson calculation of the three Landau parameters ${\mathit{F}}_{0}^{\mathit{s}}$, ${\mathit{F}}_{0}^{\mathit{a}}$, and ${\mathit{F}}_{1}^{\mathit{s}}$ of the Hubbard model for any strength of the interaction U and any filling \ensuremath{\delta}=1-n. The Landau parameter ${\mathit{F}}_{1}^{\mathit{a}}$ is then obtained by using the s-p approximation on the forward-scattering sum rule for the Landau parameters. General analytic expressions are given for the four Landau parameters and related observables. Simple asymptotic expressions for these quantities in four interesting regimes on the U,\ensuremath{\delta} manifold are presented. We also show the results of numerical calculations of these quantities for the full range of U and \ensuremath{\delta} for a system with a flat density of states, which are then compared with the experimental results for normal $^{3}\mathrm{He}$. We find good agreement with the experimentally deduced Landau parameters for both the half-filled-band model and the \ensuremath{\delta}-dependent model at reasonable values of U and \ensuremath{\delta}.

Computer simulation of hopping conductivity in lightly doped two-dimensional semiconductors

We present the results of a numerical simulation of a two-dimensional lightly doped compensated semiconductor. We choose a flat density of states with width Δε. We model the semiconductor as a Miller and Abrahams type resistor network; we use the full form of the resistance and do not take the low-temperature asymptotic form because we carry out the simulation at temperatures for which kT is of order Δε. We find that there is a wide temperature range for which [Formula: see text] with ε3 = 0.28Δε. This value of ε3 is considerably smaller than values found by others. We believe that the difference between our result and those of other workers may be attributed to their use of the low-temperature form of the resistance [Formula: see text] in a temperature range in which kT is of order Δε.

Isochromatenspektroskopische Untersuchung der Zustandsdichte der Edelmetalle

X-ray isochromats of the noble metals Cu, Ag and Au measured with high resolution are presented. In contrast with the transition metals no Ohlin-Maximum is observed. This is attributed to a relatively small and flat density of states at the Fermi edge. Published band calculations and other experimental data agree well with this result. The isochromats show broad edges at the treshold voltage. This cannot be ascribed to the temperature broadening of the Fermi limit only, but can be understood as arising from characteristic properties of the band structure of fcc metals. A short discussion of a possible connection with the so-called Li-anomaly is added.