arXiv subjects

David Nozadze

Publications and source records attributed to David Nozadze.

15 recordsLinked to original sources

arXiv2026

Intra-Pair Skew Propagation Graph (ISPG): An Analytical Model for Cascaded Channels

As data rates scale, intra-pair skew has become a critical bottleneck for high-speed differential signaling. Current analytical models are often limited, while 3D electromagnetic simulations are computationally intensive. This paper presents a comprehensive analytical framework for intra-pair skew in generic asymmetric coupled transmission lines, explicitly integrating skew into S-parameter formulations. We introduce the Intra-pair Skew Propagation Graph (ISPG), a novel graph-based methodology for calculating cumulative skew in complex, cascaded channels. The proposed framework is validated against both S-parameter simulations and empirical measurements of a 2m bulk twinax cable assembly, demonstrating excellent accuracy and robustness for high-speed interconnect design.

eess.SP↗

arXiv2025

Practical Approaches to Quantifying Intra-Pair Skew Impact via Insertion Loss Deviation

The surge in AI workloads and escalating data center requirements have created demand for ultra-high-speed interconnects exceeding 200 Gb/s. As unit intervals (UI) shrink, even a few picoseconds of intra-pair skew can significantly degrade serializer-deserializer (SerDes) performance. To quantify the impact of intra-pair skew, conventional time-domain methods are often unreliable for coupled interconnects due to skew variations across voltage levels, while frequency-domain approaches frequently fail to address reciprocity and symmetry issues. This can result in channels that meet skew specifications in one direction but not the other, despite the inherently reciprocal nature of skew impact. To address these limitations, we introduce two new reciprocal parameters for quantifying intra-pair skew effects: Skew-Induced Insertion Loss Deviation (SILD) and its complementary Figure of Merit (FOM SILD). Measurements conducted using 224 Gb/s SerDes IP and a variety of channels with different intra-pair skews demonstrate a strong correlation between FOM SILD and bit error rate (BER). Results show that when FOM SILD is below 0.2-0.3 dB, BER remains stable, indicating minimal signal integrity degradation; however, BER increases noticeably as FOM SILD exceeds 0.3 dB. Statistical analysis across more than 3,000 high-speed twinax cables reveals that the majority exhibit FOM SILD values less than 0.1 dB, underscoring the practical relevance of the proposed metrics for high-speed interconnect assessment.

eess.SP↗

arXiv2025

Skew-Induced Insertion Loss Deviation (SILD) and FOM_SILD: Metrics for Quantifying P/N Skew Effects in High-Speed Channels

The rise of AI workloads and growing data center demands have driven the need for ultra-high-speed interconnects exceeding 200 Gb/s. As unit intervals (UI) shrink, even a few picoseconds of P/N skew can degrade serializer-deserializer (SerDes) performance. Traditional methods for quantifying skew fall short in capturing its impact. We introduce two new metrics: 1) Skew-Induced Insertion Loss Deviation (SILD) and 2) its complementary Figure of Merit (FOM_SILD), analytically developed to assess P/N skew effects. Measured S-parameters confirm FOM_SILD reciprocity, while simulations of 224G PAM4 SerDes show strong correlation with bit error rate (BER) trends. This approach offers a robust framework for analyzing skew in next-generation ultra-high-speed interconnects.

eess.SY↗

arXiv2018

Finite Temperature Phase Diagrams of a Two-band Model of Superconductivity

We explore the temperature effects in the superconducting phases of a hybridized two-band system. We show that for zero hybridization between the bands, there are two different critical temperatures. However, for any finite hybridization there are only one critical temperature at which the two gaps vanish simultaneously. We construct the phase diagrams of the critical temperature versus hybridization parameter $α$ and critical temperature versus critical chemical potential asymmetry $δμ$ between the bands, identifying the superconductor and normal phases in the system. We find an interesting reentrant behavior in the superconducting phase as the parameters $α$ or $δμ$, which drive the phase transitions, increase. We also find that for optimal values of both $α$ and $δμ$ there is a significant enhancement of the critical temperature of the model.

cond-mat.supr-con↗

arXiv2017

A Two-band Model for p-wave Superconductivity

In this paper we study the effects of hybridization in the superconducting properties of a two-band system. We consider the cases that these bands are formed by electronic orbitals with angular momentum, such that, the hybridization $V(\mathbf{k})$ among them can be symmetric or antisymmetric under inversion symmetry. We take into account only intra-band attractive interactions in the two bands and investigate the appearance of an induced inter-band pairing gap. We show that (inter-band) superconducting orderings are induced in the total absence of attractive interaction between the two bands, which turns out to be completely dependent on the hybridization between them. For the case of antisymmetric hybridization we show that the induced inter-band superconductivity has a p-wave symmetry.

cond-mat.supr-con↗

arXiv2015

Compressibility as a probe of quantum phase transitions in topological superconductors

The non-Abelian statistics of Majorana fermions, their role in topological quantum computation, and the possibility of realizing them in condensed matter systems, has attracted considerable attention. While there have been recent reports of zero energy modes in single particle tunneling density of states, their identity as Majorana modes has so far not been unequivocally established. We make predictions for the local compressibility $κ_{\rm{loc}}$, tuned by changing the chemical potential $μ$ in a semiconducting nanowire with strong spin-orbit coupling and in a Zeeman field in proximity to a superconductor, that has been proposed as a candidate system for observing Majorana modes. We show that in the center of the wire, the topological phase transition is signaled by a divergence of $κ_{\rm{loc}}$ as a function of $μ$ which is an important diagnostic of the topological phase transition. We also find that a single strong impurity potential can lead to a local {\it negative} compressibility at the topological phase transition. The origin of such anomalous behavior can be traced to the formation of Andreev bound states close to topological phase transitions. Measurable by a scanning electron transistor, the compressibility includes contributions from both single particle states and collective modes and is therefore a complimentary probe from scanning tunneling spectroscopy.

cond-mat.str-el↗

arXiv2014

Topological states in normal and superconducting $p$-wave chains

We study a two-band model of fermions in a 1d chain with an antisymmetric hybridization that breaks inversion symmetry. We find that for certain values of its parameters, the $sp$-chain maps formally into a $p$-wave superconducting chain, the archetypical 1d system exhibiting Majorana fermions. The eigenspectra, including the existence of zero energy modes in the topological phase, agree for both models. The end states too share several similarities in both models, such as the behavior of the localization length, the non-trivial topological index and robustness to disorder. However, we show by mapping the $s$- and $p$- fermions to two copies of Majoranas, that the excitations in the ends of a finite $sp$ chain are indeed conventional fermions though endowed with protected topological properties. Our results are obtained by a scattering approach in a semi-infinite chain with an edge defect treated within the $T$-matrix approximation. We augment the analytical results with exact numerical diagonalization that allow us to extend our results to arbitrary parameters and also to disordered systems.

cond-mat.supr-con↗

arXiv2014

Numerical method for disordered quantum phase transitions in the large$-N$ limit

We develop an efficient numerical method to study the quantum critical behavior of disordered systems with $\mathcal{O}(N)$ order-parameter symmetry in the large$-N$ limit. It is based on the iterative solution of the large$-N$ saddle-point equations combined with a fast algorithm for inverting the arising large sparse random matrices. As an example, we consider the superconductor-metal quantum phase transition in disordered nanowires. We study the behavior of various observables near the quantum phase transition. Our results agree with recent renormalization group predictions, i.e., the transition is governed by an infinite-randomness critical point, accompanied by quantum Griffiths singularities. Our method is highly efficient because the numerical effort for each iteration scales linearly with the system size. This allows us to study larger systems, with up to 1024 sites, than previous methods. We also discuss generalizations to higher dimensions and other systems including the itinerant antiferomagnetic transitions in disordered metals.

cond-mat.stat-mech↗

arXiv2014

Contact process on generalized Fibonacci chains: infinite-modulation criticality and double-log periodic oscillations

We study the nonequilibrium phase transition of the contact process with aperiodic transition rates using a real-space renormalization group as well as Monte-Carlo simulations. The transition rates are modulated according to the generalized Fibonacci sequences defined by the inflation rules A $\to$ AB$^k$ and B $\to$ A. For $k=1$ and 2, the aperiodic fluctuations are irrelevant, and the nonequilibrium transition is in the clean directed percolation universality class. For $k\ge 3$, the aperiodic fluctuations are relevant. We develop a complete theory of the resulting unconventional "infinite-modulation" critical point which is characterized by activated dynamical scaling. Moreover, observables such as the survival probability and the size of the active cloud display pronounced double-log periodic oscillations in time which reflect the discrete scale invariance of the aperiodic chains. We illustrate our theory by extensive numerical results, and we discuss relations to phase transitions in other quasiperiodic systems.

cond-mat.stat-mech↗

arXiv2012

Modification of smeared phase transitions by spatial disorder correlations

Phase transitions in disordered systems can be smeared if rare spatial regions develop true static order while the bulk system is in the disordered phase. Here, we study the effects of spatial disorder correlations on such smeared phase transitions. The behaviors of observables are determined within optimal fluctuation theory. We show that even short-range correlations can qualitatively modify smeared phase transitions. For positive correlations (like impurity atoms attract each other), the order parameter is enhanced, while it is suppressed for repulsive correlations (like atoms repel each other). We use computer simulations to generate various types of disorder correlations, and to verify our theoretical predictions.

cond-mat.str-el↗

arXiv2012

Quantum Griffiths singularities in ferromagnetic metals

We present a theory of the quantum Griffiths phases associated with the ferromagnetic quantum phase transition in disordered metals. For Ising spin symmetry, we study the dynamics of a single rare region within the variational instanton approach. For Heisenberg symmetry, the dynamics of the rare region is studied using a renormalization group approach. In both cases, the rare region dynamics is even slower than in the usual quantum Griffiths case because the order parameter conservation of an itinerant ferromagnet hampers the relaxation of large magnetic clusters. The resulting quantum Griffiths singularities in ferromagnetic metals are stronger than power laws. For example, the low-energy density of states $ρ(ε)$ takes the asymptotic form $\exp[\{-\tildeλ\log (ε_0/ε)\}^{3/5}]/ε$ with $\tildeλ$ being non-universal. We contrast these results with the antiferromagnetic case in which the systems show power-law quantum Griffiths singularities in the vicinity of the quantum critical point. We also compare our result with existing experimental data of ferromagnetic alloy ${\rm{Ni}}_{x}{\rm{V}}_{1-x}$.

cond-mat.str-el↗

arXiv2012

Disorder correlations at smeared phase transitions

We investigate the influence of spatial disorder correlations on smeared phase transitions, taking the quantum phase transition in itinerant magnets as an example. We find that even short-range correlations can have a dramatic effect and qualitatively change the behavior of observable quantities. This is in marked contrast to conventional critical phenomena, at which short-range disorder correlations are irrelevant. We develop an optimal fluctuation theory of the quantum phase transition in the presence of correlated disorder, and we illustrate the results by computer simulations. As an experimental application, we discuss the ferromagnetic quantum phase transition in Sr$_{1-x}$Ca$_x$RuO$_3$.

cond-mat.str-el↗

arXiv2011

Non-Fermi liquid transport and "universal" ratios in quantum Griffiths phases

We use the semi-classical Boltzmann equation to investigate transport properties such as electrical resistivity, thermal resistivity, thermopower, and the Peltier coefficient of disordered metals close to an antiferromagnetic quantum phase transition. In the quantum Griffiths phase, the electrons are scattered by spin-fluctuations in the rare regions. This leads to singular temperature dependencies not just at the quantum critical point, but in the entire Griffiths phase. We show that the resulting non-universal power-laws in transport properties are controlled by the same Griffiths exponent $λ$ which governs the thermodynamics. $λ$ takes the value zero at the quantum critical point and increases throughout the Griffiths phase. We also study some of the "universal" ratios commonly used to characterize Fermi-liquid behavior.

cond-mat.str-el↗

arXiv2011

Transport properties in antiferromagnetic quantum Griffiths phases

We study the electrical resistivity in the quantum Griffiths phase associated with the antiferromagnetic quantum phase transition in a metal. The resistivity is calculated by means of the semi-classical Boltzmann equation. We show that the scattering of electrons by locally ordered rare regions leads to a singular temperature dependence. The rare-region contribution to the resistivity varies as $T^λ$ with temperature $T,$ where the $λ$ is the usual Griffiths exponent which takes the value zero at the critical point and increases with distance from criticality. We find similar singular contributions to other transport properties such as thermal resistivity, thermopower and the Peltier coefficient. We also compare our results with existing experimental data and suggest new experiments.

cond-mat.str-el↗

arXiv2011

Composition-tuned smeared phase transitions

Phase transitions in random systems are smeared if individual spatial regions can order independently of the bulk system. In this paper, we study such smeared phase transitions (both classical and quantum) in substitutional alloys A$_{1-x}$B$_x$ that can be tuned from an ordered phase at composition $x=0$ to a disordered phase at $x=1$. We show that the ordered phase develops a pronounced tail that extends over all compositions $x<1$. Using optimal fluctuation theory, we derive the composition dependence of the order parameter and other quantities in the tail of the smeared phase transition. We also compare our results to computer simulations of a toy model, and we discuss experiments.

cond-mat.str-el↗