arXiv subjects

Bhupendra Nath Tiwari

Publications and source records attributed to Bhupendra Nath Tiwari.

At least 19 recordsLinked to original sources

arXiv2019

Parameter space stability of multiple soft interactions

We study the fluctuation theory analysis of multiple soft interactions that are used to design SIBYLL 2.1 and related cosmic ray event generators. We examine fluctuation stabilities of Lund string fragmentation involving quark-antiquark and diquark-antidiquark pairs. Using the primordial transverse momentum hadron-hadron pairs, we find that the resulting Gaussian distribution yields an ill-defined ensemble under fluctuation of the model parameters of parent quark and diquarks. Further, we investigate the nature of multiple soft interactions through Pomeron-Reggeon fluctuations at various energy scales. We show that there are both stable and unstable regions under fluctuations of the Reggeon and Pomeron densities and all initial energy scales. The optimal stability zone is achieved at the Reggeon and Pomeron densities as predicted by GRV model. For hadron-hadron collisions, the limiting Gaussian profile as a function of the impact parameters of soft interactions for proton-proton collisions corresponds to an indeterminate statistical basis. Subsequently, we add higher order corrections in the Regge trajectory of constituent hadrons that play an important role in determining the shape of a proton or meson profile function in the realm of minijet model. We also discuss the accelerated nucleons with jerks and soft profile functions at off-shell-conditions. In addition, we illustrate the wall of stability/instability for multiple soft interactions by considering energy dependent soft contributions to scattering cross section as the model embedding. Qualitative discussions are provided at physical energy scales ranging from 1 GeV to 1800 GeV. This includes the analysis of CDF, P238, UA5 and ZEUS experiments.

hep-ph↗

arXiv2019

A Fluctuation Theory of Topological Susceptibility

We investigate the long-range statistical correlations, whereby discuss the nature of the undermining interacting/ noninteracting domains and associated phase transitions under variations of the quark mass and the mass scale that corresponds to renormalized pion masses and the dimensions of an ensemble of slab sub-volumes of an arbitrary simulated lattice. The purpose of this paper is to compute the system's stability and its phase structures when it's model parameters vary infinitesimally. In particular, we focus on the stability properties and phases of an arbitrary (2+1) flavor QCD configuration under fluctuations of its parameters. In order to investigate the nature of statistical and systematic errors, and the presence of noises in the system, we explore fluctuation theory equivalences of the slab sub-volume method of computing the topological susceptibility with its low energy ChPT counterpart. Hereby, we find that the ChPT configurations always correspond to a non-interacting statistical basis in the space of the quark mass and the mass scale that corresponds to renormalized pion masses. The second system as an ensemble of finite slab sub-volumes of a simulated lattice turns out to be generically interacting under fluctuations of the slab dimensions. However, it yields an ill-defined degenerate system in the infinitesimal limit of slab parameters. It is worth mentioning that implications of the intrinsic geometric analysis are well suited towards the modeling based understanding of the gluonic topological charge density fluctuations, quark mass dependence and long auto-correlation of the global topology. Finally, we discuss the stability properties of sub-volume simulated lattice improvements towards the understanding of QCD vacua, the behavior of UV divergences, finite-volume effects, statistical precision, simultaneous measurements, and associated quantum channel measurements.

hep-lat↗

arXiv2019

Stability of Gluonic Systems with Multiple Soft Interactions

In this paper, we investigate the stability properties of soft gluons in SIBYLL 2.1 with reference to its original version 1.7 that corresponds to hadronic hard interactions. In order to investigate the stability structures, we classify the regions of the gluon density fluctuations in its double leading logarithmic approximation and its equivalent description as the fractional power law. In the parameter space of initial transverse momentum $Q$ and QCD renormalization scale $L$ that correspond to extensive air showers of cosmic rays, we have categorized the surface of parameters over which the proton is stable. We further discuss the nature of local and global correlations and stability properties where the concerning statistical basis yields a stable system or undergoes a geometric phase transition. Finally, we give a phenomenological understanding towards the stability of soft interactions, Pomeron particle productions in minijet model, string fragmentation and verify our result corresponding to the experiments - CDF, P238, UAS, GEUS and UA4 collaborations.

hep-ph↗

arXiv2017

Fractional Order Heat Equation in Higher Space-Time Dimensions

In this paper, we study fractional order heat equation in higher space-time dimensions and offer specific role of heat flows in various fractional dimensions. We offer fractional solutions of the heat equations thus obtained, and examine the associated implications in various limiting cases. We anticipate perspective applications of fractional heat flow solutions in physical systems.

physics.gen-ph↗

arXiv2017

Thermodynamic Geometry of Yang-Mills Vacua

We study vacuum fluctuation properties of an ensemble of $SU(N)$ gauge theory configurations, in the limit of large number of colors, \textit{viz.} $N_c \rightarrow \infty$, and explore statistical nature of the topological susceptibility by analyzing its critical behavior at a nonzero vacuum parameter $θ$ and temperature $T$. We find that the system undergoes a vacuum phase transition at the chiral symmetry restoration temperature as well as at an absolute value of $θ$. On the other hand, the long range correlation length solely depends on $θ$ for the theories having critical exponent $e=2$ or $T=T_d+1$, where $T_d$ is the decoherence temperature. Further, it is worth noticing that the unit critical exponent vacuum configuration corresponds to a noninteracting statistical basis pertaining to a constant mass of $η^{\prime}$.

hep-th↗

arXiv2012

State-space Geometry, Statistical Fluctuations and Black Holes in String Theory

We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a new perspective of black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic state-space geometric meaning of the statistical fluctuations, local and global stability conditions and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, \textit{viz.}, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory. Keywords: Intrinsic Geometry; String Theory; Physics of black holes; Classical black holes; Quantum aspects of black holes, evaporation, thermodynamics; Higher-dimensional black holes, black strings, and related objects; Statistical Fluctuation; Flow Instability. PACS: 02.40.Ky; 11.25.-w; 04.70.-s; 04.70.Bw; 04.70.Dy; 04.50.Gh; 5.40.-a; 47.29.Ky

hep-th↗

arXiv2011

Thermodynamic Geometry and Topological Einstein-Yang-Mills Black Holes

From the perspective of the statistical fluctuation theory, we explore the role of the thermodynamic geometries and vacuum (in)stability properties for the topological Einstein-Yang-Mills black holes. In this paper, from the perspective of the state-space surface and chemical Wienhold surface, we provide the criteria for the local and global statistical stability of an ensemble of topological Einstein-Yang-Mills black holes in arbitrary spacetime dimensions $D\ge 5$. Finally, as per the formulations of the thermodynamic geometry, we offer a parametric account of the statistical consequences in both the local and global fluctuation regimes of the topological Einstein-Yang-Mills black holes.

hep-th↗

arXiv2011

On Generalized Uncertainty Principle

We study generalized uncertainty principle through the basic concepts of limit and Fourier transformation and analyze both the quantum theory of gravity and string theory from the perspective of complex function theory. Motivated from the noncommutative nature of string theory, we have proposed a UV/IR mixing dependent function $ \tildeδ(Δx,Δk, ε) $. For a given $ \tildeδ(Δx,Δk, ε) $, we arrived at the string uncertainty principle from the analyticity condition of a complex function, which depends upon UV cut-off of the theory. This non trivially modifies the quantum measurements, black hole physics and short distance geometries. The present analysis is based on the postulate that the Planck scale is the minimal length scale in nature. Furthermore, our consideration is in perfect agreement with the existence of the maximum length scale in nature. Both of the above length scales rely only upon the analysis of $ \tildeδ(Δx,Δk, ε) $ and do not directly make use of any specific structure of the theory or Hamiltonian. The Regge behavior of the string spectrum and the quantization of the horizon area of a black hole are natural consequences of the function $ \tildeδ(Δx,Δk, ε) $. It is hereby anticipated that $ \tildeδ(Δx,Δk, ε) $ contains all possible corrections operating in nature, and thus a promising possibility to reveal important clues towards the geometric origin of $M$-theory.

hep-th↗

arXiv2011

Geometric Perspective of Entropy Function: Embedding, Spectrum and Convexity

From the perspective of Sen entropy function, we study the geometric and algebraic properties of a class of (extremal) black holes in $ D \geq 4 $ spacetimes. For a given moduli space manifold, we describe the thermodynamic geometry away from attractor fixed point configurations with and without higher derivative corrections. From the notion of embedding theory, the present investigation offers a set of generalized complex structures and associated properties of differentiable manifolds. We have shown that the convexity of arbitrary entropy function can be realized in an extended subfield of the eigenvalues of the Hessian $\mathcal B$ of Sen entropy function. Thus, the spectra of $\mathcal B$ are analyzed by defining Krull of the corresponding semisymplectic algebras. From the framework of commutative algebra, we find that the convex hull of the eigenvalues defines a generalized spectrum of $\mathcal B$. The corresponding complexification is established for finitely many eigenvalues of $ \mathcal B $. For the minimally extended subfield, we show that the spectrum of $ \mathcal B $ reduces to the thermodynamic type spectra, at the attractor fixed point(s). In the limit of $ AdS_2 \times S^{D-2} $ near horizon geometry, the attractor flow analysis offers the stability of arbitrary extremal black hole. From the perspective of string compactifications, our investigation implies a set of deformed S-duality transformations, which contain both the duality invariant charges and monodromy invariant parameters. The role of the algebraic geometry is discussed towards the viewpoints of attractor stability conditions, rational conformal field theory, elliptic curves, deformed quantization(s), moduli manifolds and Calabi-Yau.

hep-th↗

arXiv2011

Sur les corrections de la géométrie thermodynamique des trous noirs

We study thermodynamic geometry of certain black holes and black branes with and without generalized uncertainty principle or stringy $ α^{\prime} $-corrections to the entropy. From this perspective, we analyze Ruppenier geometry of Reissner-Nordström black holes and show that it is well defined and corresponds to a non-interacting statistical system. We investigate that the Weinhold geometry of dilatonic black holes is regular everywhere and that of large mass Reissner-Nordström black holes in the Poincaré patch of $ AdS_4 $ contains certain narrow range of thermodynamically unstable regions in the statespace. We obtain that the generalized uncertainty principle corrected Ruppenier geometry of Reissner-Nordström black holes correspond to a non-interacting statistical system unlike the magnetically charged black holes. We show that the stringy $ α^{\prime} $-corrections do not introduce singularity in the statespace geometry of non-supersymmetric extremal black holes in $ D= 4 $. Interestingly, the degree of scalar curvature and that of the determinant of this Ruppenier geometry can be written as an integer multiple of the order of $ α^{\prime} $-correction. We further show that the statespace geometry of Gauss- Bonnet corrected supersymmetric extremal black holes in $ D=4 $ as well as non-extremal $D_1D_5$ and $D_2D_6NS_5$ black branes in $ D=10 $ is regular everywhere. Furthermore, the thermodynamic geometry of four dimensional rotating Kerr-Newman extremal black holes in Einstein-Maxwell theory is everywhere ill-defined and that of the Kaluza-Klein black holes in Einstein-Maxwell theory or the one arrising from heterotic string compactification is ill-defined only at the points of the ergo-branch.

hep-th↗

arXiv2011

On Intrinsic Geometric Stability of Controller

This work explores the role of the intrinsic fluctuations in finite parameter controller configurations characterizing an ensemble of arbitrary irregular filter circuits. Our analysis illustrates that the parametric intrinsic geometric description exhibits a set of exact pair correction functions and global correlation volume with and without the variation of the mismatch factor. The present consideration shows that the canonical fluctuations can precisely be depicted without any approximation. The intrinsic geometric notion offers a clear picture of the fluctuating controllers, which as the limit of the ensemble averaging reduce to the specified controller. For the constant mismatch factor controllers, the Gaussian fluctuations over equilibrium basis accomplish a well-defined, non-degenerate, flat regular intrinsic Riemannian surface. An explicit computation further demonstrates that the underlying power correlations involve ordinary summations, even if we consider the variable mismatch factor controllers. Our intrinsic geometric framework describes a definite character to the canonical power fluctuations of the controllers and constitutes a stable design strategy for the parameters.

stat.AP↗

arXiv2011

State-space geometry, non-extremal black holes and Kaluza-Klein monopoles

We examine the statistical nature of the charged anticharged non-extremal black holes in string theory. From the perspective of the intrinsic Riemannian Geometry, the first principle of the statistical mechanics shows that the stability properties of general nonextremal nonlarge charged black brane solutions are divulged from the positivity of the corresponding principle minors of the space-state metric tensor. Under the addition of the Kaluza-Klein monopoles, a novel aspect of the Gaussian fluctuations demonstrates that the canonical fluctuations can be ascertained without any approximation. We offer the state-space geometric implication for the most general non-extremal black brane configurations in string theory.

hep-th↗

arXiv2011

Strong Interactions, (De)coherence and Quarkonia

Quarkonia are the central objects to explore the non-perturbative nature of non-abelian gauge theories. We describe the confinement-deconfinement phases for heavy quarkonia in a hot QCD medium and thereby the statistical nature of the inter-quark forces. In the sense of one-loop quantum effects, we propose that the "quantum" nature of quark matters follows directly from the thermodynamic consideration of Richardson potential. Thereby we gain an understanding of the formation of hot and dense states of quark gluon plasma matter in heavy ion collisions and the early universe. In the case of the non-abelian theory, the consideration of the Sudhakov form factor turns out to be an efficient tool for soft gluons. In the limit of the Block-Nordsieck resummation, the strong coupling obtained from the Sudhakov form factor yields the statistical nature of hadronic bound states, e.g. kaons and Ds particles.

hep-th↗

arXiv2010

Scalar Moduli, Wall Crossing and Phenomenological Predictions

We present the scalar moduli stabilization from the perspective of the real intrinsic geometry. In this paper, we describe the physical nature of the vacuum moduli fluctuations of an arbitrary Fayet configuration. For finitely many abelian scalar fields, we show that the framework of the real intrinsic geometry investigates the mixing between the marginal and threshold vacua. Interestingly, we find that the phenomena of wall crossing and the search of the stable vacuum configurations, pertaining to $D$-term and $F$-term scalar moduli, can be accomplished for the abelian charges. For given vacuum expectation values of the moduli scalars, we provide phenomenological aspects of the vacuum fluctuations and phase transitions in the supersymmetry breaking configurations.

hep-th↗

arXiv2010

State-space Manifold and Rotating Black Holes

We study a class of fluctuating higher dimensional black hole configurations obtained in string theory/ $M$-theory compactifications. We explore the intrinsic Riemannian geometric nature of Gaussian fluctuations arising from the Hessian of the coarse graining entropy, defined over an ensemble of brane microstates. It has been shown that the state-space geometry spanned by the set of invariant parameters is non-degenerate, regular and has a negative scalar curvature for the rotating Myers-Perry black holes, Kaluza-Klein black holes, supersymmetric $AdS_5$ black holes, $D_1$-$D_5$ configurations and the associated BMPV black holes. Interestingly, these solutions demonstrate that the principal components of the state-space metric tensor admit a positive definite form, while the off diagonal components do not. Furthermore, the ratio of diagonal components weakens relatively faster than the off diagonal components, and thus they swiftly come into an equilibrium statistical configuration. Novel aspects of the scaling property suggest that the brane-brane statistical pair correlation functions divulge an asymmetric nature, in comparison with the others. This approach indicates that all above configurations are effectively attractive and stable, on an arbitrary hyper-surface of the state-space manifolds. It is nevertheless noticed that there exists an intriguing relationship between non-ideal inter-brane statistical interactions and phase transitions. The ramifications thus described are consistent with the existing picture of the microscopic CFTs. We conclude with an extended discussion of the implications of this work for the physics of black holes in string theory.

hep-th↗

arXiv2010

On Real Intrinsic Wall Crossings

We study moduli space stabilization of a class of BPS configurations from the perspective of the real intrinsic Riemannian geometry. Our analysis exhibits a set of implications towards the stability of the D-term potentials, defined for a set of abelian scalar fields. In particular, we show that the nature of marginal and threshold walls of stabilities may be investigated by real geometric methods. Interestingly, we find that the leading order contributions may easily be accomplished by translations of the Fayet parameter. Specifically, we notice that the various possible linear, planar, hyper-planar and the entire moduli space stabilities may easily be reduced to certain polynomials in the Fayet parameter. For a set of finitely many real scalar fields, it may be further inferred that the intrinsic scalar curvature defines the global nature and range of vacuum correlations. Whereas, the underlying moduli space configuration corresponds to a non-interacting basis at the zeros of the scalar curvature, where the scalar fields become un-correlated. The divergences of the scalar curvature provide possible phase structures, viz., wall of stability, phase transition, if any, in the chosen moduli configuration. The present analysis opens up a new avenue towards the stabilizations of gauge and string moduli.

hep-th↗

arXiv2010

Geometric Design and Stability of Power Networks

From the perspective of the network theory, the present work illustrates how the parametric intrinsic geometric description exhibits an exact set of pair correction functions and global correlation volume with and without the inclusion of the imaginary power flow. The Gaussian fluctuations about the equilibrium basis accomplish a well-defined, non-degenerate, curved regular intrinsic Riemannian surfaces for the purely real and the purely imaginary power flows and their linear combinations. An explicit computation demonstrates that the underlying real and imaginary power correlations involve ordinary summations of the power factors, with and without their joint effects. Novel aspect of the intrinsic geometry constitutes a stable design for the power systems.

stat.AP↗

arXiv2010

On Attractor Flow and Small Black Holes

We study the attractor flow and near horizon geometry of two-charge small black holes in heterotic string theory. The Hessian of Sen's entropy function with respect to the moduli fields has standard attractor properties and shows the interesting factorization at the attractor fixed points. We notice that the stability conditions are preserved under arbitrary $α^{\prime}$-corrections to the black hole solutions.

hep-th↗