arXiv subjects

Emiliano Papa

Publications and source records attributed to Emiliano Papa.

13 recordsLinked to original sources

arXiv2026

Analytic Pricing of Bermudan Swaptions with Few Exercise Dates

In this paper, we consider pricing a Bermudan swaption with a small number of exercise dates. We begin with the case of two exercise dates. In this limit, we show that the Bermudan price decomposes into the sum of short-dated European swaptions, setting an upper bound, minus a correction term. This correction is expressed as an integral involving a forward volatility agreement type payoff with start at the first exercise date, and it can be evaluated in closed form. The magnitude of the correction is smaller when variance is front loaded and larger when it is back-loaded. We extend to three-exercise Bermudans via backward induction under rolling forward measures. A key feature is boundary linearity enabling further analytic steps. The exercise boundary of options splits into a strike-dependent term and a variance term; together they determine optimal exercise. The linear term is negative, supressing the exponentials in subsequent steps and aiding analytic calculations. This boundary linearity extends to multiple exercise dates and yields pricing formulas with the same decomposition, showing how optionality accumulates across exercise dates. We conclude that the Bermudan can be reconstructed by adding, at each exercise date, the initial short swaption with an increasingly higher strike and subtracting the integrated payoffs of all forward-starting receiver swaptions starting at that date. The corresponding double and higher-order integrals decrease rapidly and, in the presence of only a few exercise dates, can be safely neglected without materially impacting the valuation. The general case is discussed at the end.

q-fin.CP↗

arXiv2007

Edge State Tunneling in a Split Hall Bar Model

In this paper we introduce and study the correlation functions of a chiral one-dimensional electron model intended to qualitatively represent narrow Hall bars separated into left and right sections by a penetrable barrier. The model has two parameters representing respectively interactions between top and bottom edges of the Hall bar and interactions between the edges on opposite sides of the barrier. We show that the scaling dimensions of tunneling processes depend on the relative strengths of the interactions, with repulsive interactions across the Hall bar tending to make breaks in the barrier irrelevant. The model can be solved analytically and is characterized by a difference between the dynamics of even and odd Fourier components. We address its experimental relevance by comparing its predictions with those of a more geometrically realistic model that must be solved numerically.

cond-mat.mes-hall↗

arXiv2007

Interedge coherent line junctions in Quantum Hall systems

In this paper we address some of the properties of quantum Hall line junctions (QHLJ) that occur near barriers separating electron gases on quantum Hall plateaus.In narrow barriers where electron tunneling can occur, the low energy physics of the QHLJ is described by the quantum sine-Gordon model. We propose procedures to study a sort of properties of these systems in relation with recent experimental studies of Kang {\it et al.}, Nature {\bf 403}, 59 (2000). We propose experimental ways of measuring the values of the dimensionless coupling constant characteristic for the Sine-Gordon model as well as its Fermi velocity. When the bulk filling of the 2DEG subsystems is $ν\sim 2$, these systems can be good candidates for observation of spin-incoherent LL behavior.

cond-mat.mes-hall↗

arXiv2007

Electrostatics of Edge States of Quantum Hall Systems with Constrictions: Metal--Insulator Transition Tuned by External Gates

The nature of a metal--insulator transition tuned by external gates in quantum Hall (QH) systems with point constrictions at integer bulk filling, as reported in recent experiments of Roddaro et al. [1], is addressed. We are particularly concerned here with the insulating behavior--the phenomena of backscattering enhancement induced at high gate voltages. Electrostatics calculations for QH systems with split gates performed here show that observations are not a consequence of interedge interactions near the point contact. We attribute the phenomena of backscattering enhancement to a splitting of the integer edge into conducting and insulating stripes, which enable the occurrence of the more relevant backscattering processes of fractionally charged quasiparticles at the point contact. For the values of the parameters used in the experiments we find that the conducting channels are widely separated by the insulating stripes and that their presence alters significantly the low-energy dynamics of the edges. Interchannel impurity scattering does not influence strongly the tunneling exponents as they are found to be irrelevant processes at low energies. Exponents of backscattering at the point contact are unaffected by interchannel Coulomb interactions since all channels have same chirality of propagation.

cond-mat.mes-hall↗

arXiv2006

Thermodynamics of the Double-Layer Quantum Hall Systems

In this paper we apply the exact solution of the sine-Gordon model to describe thermodynamic properties of the soliton liquid in the incommensurate phase of the double-layer quantum Hall systems. In this way we include thermal fluctuations and extend to finite temperatures the results obtained by C.B. Hanna, A.H. MacDonald and S.M. Girvin [Phys. Rev. B {\bf 63}, 125305 (2001)]. In addition we calculate the specific heat of the system. While the results obtained for the sine-Gordon model are available in a temperature interval $(0,T_c)$, where $T_c=8πρ_s$, $ρ_s$ the pseudospin stiffness, they can be applied in the bilayer system up to temperatures $3T_{\rm BKT}$, where $T_{\rm BKT}=πρ_s/2$ is the vortex mediated Berezinskii-Kosterlitz-Thouless transition temperature. Above this temperature the operators $\cosβϕ$ and $\cos(2π\vartheta/β)$ are both relevant and the system is in a phase with coexisting order parameters. $\vartheta$ is the dual field of $ϕ$ and $β$ is the sine-Gordon coupling constant. We provide numerical estimates for thermodynamic quantities for the range of parameters relevant for GaAs.

cond-mat.str-el↗

arXiv2006

Metal-Insulator Transition Tuned by External Gates in Hall Systems with Constrictions

The nature of a metal-insulator transition tuned by external gates in quantum Hall (QH) systems with point constrictions, as reported in recent experiments of Roddaro et al [1], is examined. We attribute this phenomenon to a splitting of the integer edge into conducting and insulating stripes, the latter wide enough to allow for the stability of the edge structure. Inter-channel impurity scattering and inter-channel Coulomb interactions do not destabilize this picture.

cond-mat.str-el↗

arXiv2005

Edge Magnetoplasmons in Quantum Hall Line Junction Systems

A quantum Hall line junction system consists of a one-dimensional Luttinger liquid (LL) and two chiral channels that allow density waves incident upon and reflected by the LL to be measured separately. We demonstrate that interactions in a quantum Hall line junction system can be probed by studying edge magnetoplasmon absorption spectra and their polarization dependences. Strong interactions in the junction lead to collective modes that are isolated in either Luttinger liquid or contact subsystems.

cond-mat.mes-hall↗

arXiv2004

Nonuniversal properties of the single-particle density of states of 1D system with electron-phonon interactions

We have calculated the single-particle density of states (DOS) for a model of spinfull Tomonaga-Luttinger liquid with frequency dependent parameter $K_c$ of the charge sector (and $K_s=1$ of spin sector).Such frequency dependence may originate from interactions withoptical phonons.DOS exhibits a power-low suppressed asymptotic behaviour near $ω=0$ with exponent largerthan one, in agreement with previous results. For larger frequencies, but stillnot far away from the origin,DOS exhibits a peak, the position of which scales as$[K(0)+K^{-1}(0)]ω_0$, where $ω_0$ is the characteristic phononfrequency. The position of the peak decreases as the phonon'sfrequency becomes smaller. It is interesting that the peak of DOS does not coincide with the characteristic phonon frequency.

cond-mat.str-el↗

arXiv2004

Interactions suppress Quasiparticle Tunneling at Hall Bar Constrictions

Tunneling of fractionally charged quasiparticles across a two-dimensional electron system on a fractional quantum Hall plateau is expected to be strongly enhanced at low temperatures. This theoretical prediction is at odds with recent experimental studies of samples with weakly-pinched quantum-point-contact constrictions, in which the opposite behavior is observed. We argue here that this unexpected finding is a consequence of electron-electron interactions near the point contact.

cond-mat.supr-con↗

arXiv2002

Quantum theory of bilayer quantum Hall smectics

Mean-field theory predicts that bilayer quantum Hall systems at odd integer total filling factors can have stripe ground states in which the top Landau level is occupied alternately by electrons in one of the two layers. We report on an analysis of the properties of these states based on a coupled Luttinger liquid description that is able to account for quantum fluctuations of charge-density and position along each stripe edge. The soft modes associated with the broken symmetries of the stripe state lead to an unusual coupled Luttinger liquid system with strongly enhanced low-temperature heat capacity and strongly suppressed low-energy tunneling density of states. We assess the importance of the intralayer and interlayer back-scattering terms in the microscopic Hamiltonian, which are absent in the Luttinger liquid description, by employing a perturbative renormalization group approach which re-scales time and length along but not transverse to the stripes. With interlayer back-scattering interactions present the Luttinger liquid states are unstable either to an incompressible striped state that has spontaneous interlayer phase coherence and a sizable charge gap even at relatively large layer separations, or to Wigner crystal states. Our quantitative estimates of the gaps produced by back-scattering interactions are summarized in Fig. [phase_diagram] by a schematic phase diagram intended to represent predicted experimental findings in very high mobility bilayer systems at dilution refrigerator temperatures as a function of layer separation and bilayer density balance.

cond-mat.str-el↗

arXiv2000

Scaling Exponents in the Incommensurate Phase of the Sine-Gordon and U(1) Thirring Models

In this paper we study the critical exponents of the quantum sine-Gordon and U(1) Thirring models in the incommensurate phase. This phase appears when the chemical potential $h$ exceeds a critical value and is characterized by a finite density of solitons. The low-energy sector of this phase is critical and is described by the Gaussian model (Tomonaga-Luttinger liquid) with the compactification radius dependent on the soliton density and the sine-Gordon model coupling constant $β$. For a fixed value of $β$, we find that the Luttinger parameter $K$ is equal to 1/2 at the commensurate-incommensurate transition point and approaches the asymptotic value $β^2/8π$ away from it. We describe a possible phase diagram of the model consisting of an array of weakly coupled chains. The possible phases are Fermi liquid, Spin Density Wave, Spin-Peierls and Wigner crystal.

cond-mat.str-el↗

arXiv2000

A Pseudogap in the Single-Particle Density of States of a Tomonaga-Luttinger Liquid

We study a single-particle density of states (DOS) in a model of Tomonaga-Luttinger liquid with small (large) values of the Luttinger parameter $K_\rc < 0.17$, ($K_\rc > 5.82$), in the charge sector. We explain that such values of $K_\rc$ may be achieved by electron-phonon interactions without generating the spin gap. We suggest that electron-phonon interactions can be partially incorporated into the Tomonaga-Luttinger liquid scheme by introducing frequency dependent $K_\rc(ω)$. We demonstrate that when the low-frequency asymptotic value $K_\rc(0) < 0.17$ or $K_\rc(0) > 5.82$, the single-particle DOS has a pseudogap behavior in frequency where $ρ(ω)/ω$ vanishes at small frequencies. The DOS exhibits a peak the position of which scales as $[K(0) + K^{-1}(0)]ω_0/2$ where $ω_0$ is the characteristic phonon frequency.

cond-mat.str-el↗

arXiv1999

Exact Results for Thermodynamics of the Classical Field Theories: Sine- and Sinh-Gordon Models

Using the recently obtained exact results for the expectation values of operators in the sine- and sinh-Gordon models [A. B. Zamolodchikov and S. Lukyanov, Nucl. Phys. B{\bf 493}, 571 (1997), V. Fateev, S. Lukyanov, A. B. Zamolodchikov and Al. B. Zamolodchikov, Phys. Lett. B{\bf 406}, 83 (1997)] we calculate the specific heat of the corresponding two dimensional Euclidean (classical) models. We show that the temperature dependence of the specific heat of the sine-Gordon model, in the commensurate phase, has a maximum well below the Kosterlitz-Thouless transition and that the sinh-Gordon model is thermodynamically unstable in the strong coupling regime. We give also the temperature dependence of the specific heat in the incommensurate phase of the sine-Gordon model.

cond-mat.str-el↗