Rm El Research Articles

Conductivity, diffusivity, and violation of the Wiedemann-Franz Law in a hadron resonance gas with van der Waals interactions

In this work, a hadron resonance gas under van der Waals (VDW) interactions has been studied. Both attractive and repulsive interactions between the meson-meson and (anti)baryon-(anti)baryon have been taken into consideration. Various transport properties such as electrical conductivity ($\sigma_{\rm el}$) and thermal conductivity ($\kappa_{\rm th}$) have been estimated by solving the Boltzmann transport equation under the relaxation time approximation. The effect of baryochemical potential ($\mu_{\rm B}$) and temperature is also explicitly explored for the mentioned observables. Comparisons have been made with the results obtained from other existing theoretical models. We observe the violation of Wiedemann-Franz law in a hadron resonance gas at a high-temperature regime. The corresponding diffusivities have also been estimated, which can help us to understand the system in a better way.

Cumulative effects of collision integral, strong magnetic field, and quasiparticle description on charge and heat transport in a thermal QCD medium

Our first aim is to explore the effect of the collision integral with the insurance of instantaneous conservation of particle number on charge and heat transport in a thermal QCD medium. The second aim is to see how the dimensional reduction due to strong magnetic field (B) modulates the transport through the entangled effects, {\em such as} collision-time and occupation probability etc. in collision integral. The final aim is to check how the quasiparticle description through dispersion relation of thermal QCD in strong B, alters the aforesaid conclusions. We observe that modified collision term expedites both transport, which is manifested by large magnitudes of electrical ($\sigma_{\rm el}$) and thermal ($\kappa$) conductivities, in comparison to relaxation-collision term. As a corollary, Lorenz number is dominated by the later and Knudsen number is by the former. However, strong B not only flips the dominance of collision term in heat transport, it also causes drastic enhancement of both $\sigma_{\rm el}$ and $\kappa$ and reduction in specific heat. As a result, the equilibration factor, Knudsen number becomes much larger than one, which defies physical interpretation. Finally, quasiparticle description in the absence of strong B impedes the transport of charge and heat, resulting in the meagre decrease of conductivities, however, strong B does noticeable observations: conductivities now gets reduced to physically plausible values, T-dependence of $\sigma_{\rm el}$ gets reversed, {\em i.e.} it now decreases with T, effect of collision integral gets smeared in $\kappa$ etc. Knudsen number thus becomes much smaller than one, implying that the system be remained in equilibrium. These findings attribute to the fact that the collective modes in the dispersion relation of thermal QCD in strong B sets in much larger scale, manifested by large in-medium masses.

Momentum and its affiliated transport coefficients for hot QCD matter in a strong magnetic field

We have studied the effects of anisotropies on the momentum transport in a QCD matter by shear ($\eta$) and bulk ($\zeta$) viscosities. The anisotropies arise either by the strong magnetic field or by the preferential expansion. This study helps to understand the fluidity and location of transition point of matter through $\eta/s$ and $\zeta/s$ ($s$ is entropy density), respectively, the sound attenuation through the Prandtl number (Pl), the nature of flow by the Reynolds number (Rl), and the competition between momentum and charge diffusions. The viscosities are calculated in the relaxation time approximation of kinetic theory within the quasiparticle model. Compared to isotropic medium, both $\eta$ and $\zeta$ get increased in magnetic field-driven (B-driven) anisotropy, contrary to the decrease in expansion-driven anisotropy. $\eta$ increases with temperature faster in former case than in latter case whereas $\zeta$ in former case decreases with temperature and in latter case, it is meagre and diminishes at a specific temperature. So the viscosities can distinguish aforesaid anisotropies. Thus, $\eta/s$ gets enhanced in former case and in latter case, it becomes smaller than isotropic one. Similarly $\zeta/s$ gets amplified but decreases faster with the temperature in a strong magnetic field. The Prandtl number gets increased in B-induced anisotropy and gets decreased in expansion-induced anisotropy, compared to isotropic one. Since, Pl is found larger than 1, the sound attenuation is governed by momentum diffusion. The B-driven anisotropy makes the Reynolds number smaller than one, whereas the expansion-driven anisotropy makes it larger. The ratio ($\frac{\eta}{s}/\frac{\sigma_{\rm el}}{T}$) gets amplified in B-driven anisotropy whereas it gets reduced in expansion-driven anisotropy. Since, the ratio is always more than one, the momentum diffusion prevails over the charge diffusion.

New parton model for the soft interactions at high energies: The odderon

In this paper we discuss the Odderon contribution in our model[19] that gives a fairly good description of $\sigma_{\rm tot}$ $\sigma_{\rm el}$and $B_{\rm el}$ for proton-proton scattering. We show that the shadowing corrections are large, and induce considerable dependence on energy for the Odderon contribution, which in perturbative QCD does not depend on energy. This energy dependence is in agreement with the experimental data for $\rho = {\rm Re}/{\rm Im}$, assuming that the Odderon gives a contribution of about 1 mb at W = 7 TeV. This differs greatly with our estimates for a CGC based model. We reproduce the main features of the $ t$ -dependence that are measured experimentally: the slope of the elastic cross section at small $t$, the existence of the minima in $t$-dependence which is located at $|t|_{min}$ = 0.52 GeV 2 at W= 7 TeV; and the behaviour of the elastic cross section at $ |t| > |t|_{min}$.The real part of the elastic amplitude turns out to be much smaller than the experimental one. Consequently, to achieve a description of the data, it is necessary to add an odderon contribution.

Revisit to electrical and thermal conductivities, Lorenz and Knudsen numbers in thermal QCD in a strong magnetic field

We have explored how the electrical ($\sigma_{\rm el}$) and thermal ($\kappa$) conductivities in a thermal QCD medium get affected in weak-momentum anisotropies arising either due to a strong magnetic field or due to asymptotic expansion. This study facilitates to understand the longevity of strong magnetic field through $\sigma_{el}$, Lorenz number in Wiedemann-Franz law, and the validity of equilibrium by the Knudsen number. We calculate the conductivities by solving relativistic Boltzmann transport equation in relaxation-time approximation within quasiparticle model at finite T and strong B. We have found that $\sigma_{el}$ and $\kappa$ get enhanced in a magnetic field-driven anisotropy, but $\sigma_{el}$ decreases with temperature, opposite to its faster increase in expansion-driven anisotropy. Whereas $\kappa$ increases slowly with temperature, contrary to its rapid increase in expansion-driven anisotropy. The above findings are broadly attributed to three factors: the stretching and squeezing of distribution function in anisotropies generated by the magnetic field and asymptotic expansion, respectively, the dispersion relation and resulting phase-space factor, the relaxation-time in absence and presence of strong magnetic field. So $\sigma_{\rm el}$ extracts the time-dependence of magnetic field, which decays slower than in vacuum but expansion-driven anisotropy makes the decay faster. The variation in $\kappa$ transpires that Knudsen number decreases with T but expansion-driven anisotropy reduces its value and magnetic field-driven anisotropy raises its value but to less than one, thus the system can still be in equilibrium. The ratio, $\kappa/\sigma_{el}$ in magnetic field-driven anisotropy increases linearly with temperature but with a value smaller than in expansion-driven anisotropy. Thus the Lorenz number can make the distinction between different anisotropies.

Thermodynamic signatures of quantum criticality in cuprate superconductors

The three central phenomena of cuprate (copper oxide) superconductors are linked by a common doping level p*-at which the enigmatic pseudogap phase ends and the resistivity exhibits an anomalous linear dependence on temperature, and around which the superconducting phase forms a dome-shaped area in the phase diagram1. However, the fundamental nature of p* remains unclear, in particular regarding whether it marks a true quantum phase transition. Here we measure the specific heat C of the cuprates Eu-LSCO and Nd-LSCO at low temperature in magnetic fields large enough to suppress superconductivity, over a wide doping range2 that includes p*. As a function of doping, we find that Cel/T is strongly peaked at p*(where Cel is the electronic contribution to C) and exhibits a log(1/T) dependence as temperature T tends to zero. These are the classic thermodynamic signatures of a quantum critical point3-5, as observed in heavy-fermion6 and iron-based7 superconductors at the point where their antiferromagnetic phase comes to an end. We conclude that the pseudogap phase of cuprates ends at a quantum critical point, the associated fluctuations of which are probably involved in d-wave pairing and the anomalous scattering of charge carriers.

Electrical conductivity of hot and dense QCD matter created in heavy-ion collisions: A color string percolation approach

Recently, transport coefficients viz. shear viscosity, electrical conductivity etc. of strongly interacting matter produced in heavy-ion collisions have drawn considerable interest. We study the normalised electrical conductivity ($\sigma_{\rm el}$/T) of hot QCD matter as a function of temperature (T) using the Color String Percolation Model (CSPM). We also study the temperature dependence of shear viscosity and its ratio with electrical conductivity for the QCD matter. We compare CSPM estimations with various existing results and lattice Quantum Chromodynamics (lQCD) predictions with (2+1) dynamical flavours. We find that $\sigma_{\rm el}$/T in CSPM has a very weak dependence on the temperature. We compare CSPM results with those obtained in Boltzmann Approach to Multi-Parton Scatterings (BAMPS) model. A good agreement is found between CSPM results and predictions of BAMPS with fixed strong coupling constant.

Collision cross sections for the thermalization of cold gases

The collision cross section that controls thermalization of gas mixtures is the transport cross section $\sigma_\eta^{(1)}$ and not the elastic cross section $\sigma_{\rm el}$. The two are the same for pure s-wave scattering but not when higher partial waves contribute. We investigate the differences between them for prototype atomic mixtures and show that the distinction is important at energies above 100 $\mu$K for LiYb and 3 $\mu$K for RbYb and RbCs. For simple systems both $\sigma_\eta^{(1)}$ and $\sigma_{\rm el}$ follow universal energy dependence that depends only on the s-wave scattering length when expressed in reduced length and energy units.

Superconducting specific-heat jumpΔCel∝Tcβ(β≈2)forK1−xNaxFe2As2

We present a systematic study of the electronic specific heat jump ($\Delta C_{\rm el}$) at the superconducting transition temperature $T_c$ of K$_{1-x}$Na$_x$Fe$_2$As$_2$. Both $T_c$ and $\Delta C_{\rm el}$ monotonously decrease with increasing $x$. The specific heat jump scales approximately with a power-law, $\Delta C_{\rm el} \propto T_c^{\beta}$, with $\beta \approx 2$ determined by the impurity scattering rate, in contrast to most iron-pnictide superconductors, where the remarkable Bud'ko-Ni-Canfield (BNC) scaling $\Delta C_{\rm el} \propto T^3$ has been found. Both the $T$ dependence of $C_{\rm el}(T)$ in the superconducting state and the nearly quadratic scaling of $\Delta C_{\rm el}$ at $T_c$ are well described by the Eliashberg-theory for a two-band $d$-wave superconductor with weak pair-breaking due to nonmagnetic impurities. The disorder induced by the Na substitution significantly suppresses the small gaps leading to gapless states in the slightly disordered superconductor, which results in a large observed residual Sommerfeld coefficient in the superconducting state for $x > 0$.

Forward hadronic scattering at 8 TeV: Predictions for the LHC

The Large Hadron Collider (LHC) recently started operating at 8 TeV. In this note, we update our earlier LHC forward hadronic scattering predictions \cite{physicsreports,update7, blackdisk}, giving new predictions, including errors, for the $pp$ total and inelastic cross sections, the $\rho$-value, the nuclear slope parameter $B$, $d\sigma_{\rm el}/dt$, and the large gap survival probability at 8 TeV.

Ni-impurity effects on the superconducting gap of La2−xSrxCuO4studied from the magnetic field and temperature dependence of the electronic specific heat

The magnetic field and temperature dependence of the electronic specific heat $C_{\rm el}$ have been systematically investigated in $\rm La_{2-{\it x}}Sr_{\it x}Cu_{1-{\it y}}Ni_{\it y}O_4$ (LSCNO) in order to study Ni-impurity effects on the superconducting (SC) gap. In LSCNO with $x$=0.15 and $y$=0.015, the value of $\gamma$ ($\equiv C_{\rm el}/T$) at $T$=0 K, $\gamma_0$, is enhanced under the magnetic field $H$ applied along the $\bm c$-axis. The increment of $\gamma_0$, $\Delta \gamma_0$, follows the Volovik relation $\Delta \gamma_0$=$A\sqrt{H}$, characteristic of the SC gap with line nodes, with prefactor $A$ similar to that of a pure sample. The $C_{\rm el}/T$ vs. $T$ curve under $H$=0 shows a d-wave-like SC anomaly with an abrupt increase at $T_{\rm c}$ and $T$-linear dependence at $T$$\ll$$T_{\rm c}$, although the $\gamma_0$-value in the $C_{\rm el}/T$ vs. $T$ curve increases with increasing Ni concentrations. Interestingly, as the SC part of $C_{\rm el}/T$, $C_{\rm el}/T$$-$$\gamma_0$$\equiv$$\gamma_{\rm s}$, decreases in LSCNO, $T_{\rm c}$ is reduced in proportion to the decrease of $\gamma_{\rm s}$. These findings can be explained phenomenologically by a simple model in which Ni impurities bring about strong pair breaking at the edges of the coherent nodal part of the Fermi surface but in the vicinity of the nodes of the SC gap. The reduction of the SC condensation energy $U_0$ in LSCNO, evaluated from $C_{\rm el}$ at $T$ {0.3em}\raisebox{0.4ex}{$<$} {-0.75em}\raisebox{-.7ex}{$\sim$} {0.3em}$T_{\rm c}$, is also understood by the same model.

Forward hadronic scattering at 7 TeV: An update on predictions for the LHC

The LHC has successfully run for a long period at half energy, 7 TeV. In this note, we update earlier full-energy Large Hadron Collider (LHC) forward hadronic scattering predictions \cite{physicsreports}, giving new predictions, including errors, for the $pp$ total and inelastic cross sections, the $\rho$-value, the nuclear slope parameter $B$, $d\sigma_{\rm el}/dt$, and the large gap survival probability at the current 7 TeV energy.

Nuclear contribution to the specific heat of Yb(Rh0.93Co0.07)2Si2

AbstractSpecific heat measurements of a Yb(Rh0.93Co0.07)2Si2 high‐quality single crystal in magnetic fields $0.5 \leq \mu _0 H \leq 10$ T and in the temperature range between 0.05 and 4 K are presented. To extract the electronic specific heat Cel from the raw data, and consequently the temperature dependence of the Sommerfeld coefficient $\gamma = {{C_{{\rm el}} } \mathord{\left/ {\vphantom {{C_{{\rm el}} } T}} \right. \kern-\nulldelimiterspace} T}$, the nuclear magnetic and electric contributions to the specific heat have been evaluated. The error between the experimental data below 1 K and the theoretical calculation varies between 0.9 and 8.7%, indicating that the coefficients used in our model are accurate and appropriate. The high‐field ground state is confirmed to be a Fermi liquid. This analysis allows to determine the H‐dependence of γ for fields larger than 0.5 T and its change across the anomaly at $\mu _0 H_0 \approx 5.8$ T.

Some properties of essential spectra of a positive operator, II

Let T be a positive operator on a Banach lattice E. Some properties of Weyl essential spectrum σew(T), in particular, the equality \(\sigma_{\rm ew}(T) = \bigcap\limits_{0 \le K \in \mathcal {K} (E)} \sigma(T + K)\), where \(\mathcal {K}(E)\) is the set of all compact operators on E, are established. If r(T) does not belong to Fredholm essential spectrum σef(T), then \(r(T) \notin \sigma(T + a|T_{-1}|)\) for every a ≠ 0, where T−1 is a residue of the resolvent R(., T) at r(T). The new conditions for which \(r(T) \notin \sigma_{\rm ef}(T)\) implies \(r(T) \notin \sigma_{\rm ew}^-(T) = \bigcap\limits_{0 \le K \in {\mathcal K}(E) \le T} \sigma(T - K)\), are derived. The question when the relation \(\sigma_{\rm ew}(T) \subseteq \sigma_{\rm el}(T)\) holds, where \(\sigma_{\rm el}(T) = \bigcap\limits_{0 \le Q \le T \atop Q \le K \in {\mathcal K}(E)}\sigma(T - Q)\) is Lozanovsky’s essential spectrum, will be considered. Lozanovsky’s order essential spectrum is introduced. A number of auxiliary results are proved. Among them the following generalization of Nikol’sky’s theorem: if T is an operator of index zero, then T = R + K, where R is invertible, K ≥ 0 is of finite rank. Under the natural assumptions (one of them is \(r(T) \notin \sigma_{\rm ef}(T)\)) a theorem about the Frobenius normal form is proved: there exist T-invariant bands \(E = B_n \supseteq B_{n - 1} \supseteq \cdots \supseteq B_0 = \{0\}\) such that if \(r(P_{D_i}TP_{D_i}) = r(T)\), where \(D_i = B_i \cap B_{i - 1}^{\rm d}\), then an operator \(P_{D_i}TP_{D_i}\) on Di is band irreducible.

Numerical renormalization group approach to a quartet quantum-dot array connected to reservoirs: Gate-voltage dependence of the conductance

The ground-state properties of quartet quantum-dot arrays are studied using the numerical renormalization group (NRG) method with a four-site Hubbard model connected to two non-interacting leads. Specifically, we calculate the conductance and local charge in the dots from the many-body phase shifts, which can be deduced from the fixed-point eigenvalues of NRG. As a function of the on-site energy $\epsilon_d$ which corresponds to the gate voltage, the conductance shows alternatively wide peak and valley. Simultaneously, the total number of electrons $N_{\rm el}$ in the four dots shows a quantized stair case behavior due to a large Coulomb interaction $U$. The conductance plateaus of the Unitary limit emerging for odd $N_{\rm el}$ are caused by the Kondo effect. The valleys of the conductance emerge for even $N_{\rm el}$, and their width becomes substantially large at half-filling. It can be regarded as a kind of the Mott-Hubbard insulating behavior manifesting in a small system. These structures of the plateaus and valleys become weak for large values of the hybridization strength $\Gamma$ between the chain and leads. We also discuss the parallel conductance for the array connected to four leads.

Scaling properties of one-dimensional Anderson models in an electric field: Exponential versus factorial localization

We investigate the scaling properties of eigenstates of a one-dimensional (1D) Anderson model in the presence of a constant electric field. The states show a transition from exponential to factorial localization. For infinite systems this transition can be described by a simple scaling law based on a single parameter $\lambda_{\infty} = l_{\infty}/l_{\rm el}$, the ratio between the Anderson localization length $l_{\infty}$ and the Stark localization length~$l_{\rm el}$. For finite samples, however, the system size $N$ enters the problem as a third parameter. In that case the global structure of eigenstates is uniquely determined by two scaling parameters $\lambda_N=l_\infty/N$ and $\lambda_\infty=l_\infty/l_{\rm el}$.