arXiv subjects

P. G. Silvestrov

Publications and source records attributed to P. G. Silvestrov.

50 records · Page 3Linked to original sources

arXiv1998

Localization in an imaginary vector potential

Eigenfunctions of 1d disordered Hamiltonian with constant imaginary vector potential are investigated. Even within the domain of complex eigenvalues the wave functions are shown to be strongly localized. However, this localization is of a very unusual kind. The logarithm of the wave function at different coordinates $x$ fluctuates strongly (just like the position of Brownian particle fluctuates in time). After approaching its maximal value the logarithm decreases like the square root of the distance $\bar{(\ln|ψ_{max}/ψ|)^2} \sim |x-x_0|$. The extension of the model to the quasi-1d case is also considered.

cond-mat.mes-hall↗

arXiv1998

Vortices in a cylinder: Localization after depinning

Edge effects in the depinned phase of flux lines in hollow superconducting cylinder with columnar defects and electric current along the cylinder are investigated. Far from the ends of the cylinder vortices are distributed almost uniformly (delocalized). Nevertheless, near the edges these free vortices come closer together and form well resolved dense bunches. A semiclassical picture of this localization after depinning is described. For a large number of vortices their density $ρ(x)$ has square root singularity at the border of the bunch ($ρ(x)$ is semicircle in the simplest case). However, by tuning the strength of current, the various singular regimes for $ρ(x)$ may be reached. Remarkably, this singular behaviour reproduces the phase transitions discussed during the past decade within the random matrix regularization of 2d-Gravity.

cond-mat.stat-mech↗

arXiv1997

Thermopower of Single-Channel Disordered and Chaotic Conductors

We show (analytically and by numerical simulation) that the zero-temperature limit of the distribution of the thermopower S of a one-dimensional disordered wire in the localized regime is a Lorentzian, with a disorder-independent width of 4 pi^3 k_B^2 T/3eΔ(where T is the temperature and Δthe mean level spacing). Upon raising the temperature the distribution crosses over to an exponential form exp(-2|S|eT/Δ). We also consider the case of a chaotic quantum dot with two single-channel ballistic point contacts. The distribution of S then has a cusp at S=0 and a tail |S|^{-1-β} log|S| for large S (with β=1,2 depending on the presence or absence of time-reversal symmetry).

cond-mat.dis-nn↗

arXiv1997

Decay of Quasi-Particle in a Quantum Dot: the role of Energy Resolution

The disintegration of quasiparticle in a quantum dot due to the electron interaction is considered. It was predicted recently that above the energy $\eps^{*} = Δ(g/\ln g)^{1/2}$ each one particle peak in the spectrum is split into many components ($Δ$ and $g$ are the one particle level spacing and conductance). We show that the observed value of $\eps^{*}$ should depend on the experimental resolution $δ\eps$. In the broad region of variation of $δ\eps$ the $\ln g$ should be replaced by $\ln(Δ/ gδ\eps)$. We also give the arguments against the delocalization transition in the Fock space. Most likely the number of satellite peaks grows continuously with energy, being $\sim 1$ at $\eps \sim \eps^{*}$, but remains finite at $\eps > \eps^{*}$. The predicted logarithmic distribution of inter-peak spacings may be used for experimental confirmation of the below-Golden-Rule decay.

cond-mat.mes-hall↗

arXiv1997

High order corrections to the Renormalon

The high order corrections to renormalon are considered. Each new type of insertions into the renormalon chain of graphs generates the correction to the asymptotics of perturbation theory of the order of $\sim 1$. However, this series of corrections to the asymptotics is not the asymptotic one (i.e. the $m$-th correction does not grow like $m!$). The summation of these corrections for UV renormalon may change the asymptotics by factor $N^δ$. For the traditional IR renormalon the $m$-th correction diverges like $(-2)^m$. However, this divergency has no infrared origin and may be removed by proper redefinition of IR renormalon. On the other hand for IR renormalons in hadronic event shapes one should naturally expect these multi-loop contributions to decrease like $(-2)^{-m}$. Some problems expected upon reaching the best accuracy of perturbative QCD are also discussed.

hep-ph↗

arXiv1997

Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement

Coherent propagation of two interacting particles in $1d$ weak random potential is considered. An accurate estimate of the matrix element of interaction in the basis of localized states leads to mapping onto the relevant matrix model. This mapping allows to clarify the mechanism of enhancement of the localization length which turns out to be rather different from the one considered in the literature. Although the existence of enhancement is transparent, an analytical solution of the matrix model was found only for very short samples. For a more realistic situation numerical simulations were performed. The result of these simulations is consistent with l_{2}/l_1 \sim l_1^γ , where $l_1$ and $l_2$ are the single and two particle localization lengths and the exponent $γ$ depends on the strength of the interaction. In particular, in the limit of strong particle-particle interaction there is no enhancement of the coherent propagation at all ($l_{2} \approx l_1$).

cond-mat.stat-mech↗

arXiv1997

Theory of directed localization in one dimension

We present an analytical solution of the delocalization transition that is induced by an imaginary vector potential in a disordered chain [N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996), cond-mat/9603165]. We compute the relation between the real and imaginary parts of the energy in the thermodynamic limit, as well as finite-size effects. The results are in good agreement with numerical simulations for weak disorder (mean free path large compared to the wavelength).

cond-mat.mes-hall↗

arXiv1997

Summing graphs for random band matrices

A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix model regularization of 2d-gravity, turns out to be very useful for band matrices. The critical behavior at the edge of spectrum and the asymptotics of energy level correlation function are considered. This correlation function together with the hypothesis about universality of spectral correlations allows to estimate easily the localization length for eigen-vectors. A smoothed two-point correlation function of local density of states $\overline{ ρ(E_1,i) ρ(E_2,j)_c}$ as well as the energy level correlation for finite size band matrices are also found. As d-dimensional generalization of band matrices lattice Hamiltonians with long-range random hopping are considered as well.

cond-mat.stat-mech↗

arXiv1995

The Status of Renormalon

It is shown that the series of renormalon--type graphs, which consist in the chain of insertions to one soft(hard) gluon(photon) line is in fact ill defined. Each new type of insertions, which appears in the higher orders of perturbation theory, generates the correction to renormalon of the order of $\sim 1$. However, this series of the corrections to the asymptotics although have no small parameter but hopefully is not the asymptotic one. The consideration based on the use of the renormalization group equation for effective charge is supported by the direct diagrammatic picture.

hep-ph↗

arXiv1995

Instanton--anti-instanton pair induced contributions to $R_{e^+e^-\to hadrons}$ and $R_{τ\to hadrons}$

The instanton--anti-instanton pair induced asymptotics of perturbation theory expansion for the cross section of electron--positron pair annihilation to hadrons and hadronic width of $τ$-lepton was found. For $N_f = N_c$ the nonperturbative instanton contribution is finite and may be calculated without phenomenological input. The instanton induced peturbative asymptotics was shown to be enhanced as $(n+10)!$ and in the intermediate region $n<15$ may exceed the renormalon contribution. Unfortunately, the analysis of $\sim 1/n$ corrections shows that for $n \sim 10$ the obtained asymptotic expressions are at best only the order of magnitude estimate. The asymptotic series for $R_{e^+ e^- \rightarrow hadrons}$ , though obtained formally for $N_f =N_c$, is valid up to energies $\sim 15$Gev. The instanton--anti-instanton pair nonperturbative contribution to $R_{τ\rightarrow hadrons}$ blows up. On the one hand, this means that instantons could not be considered {\it ab--initio} at such energies. On the other hand, this result casts a strong doubt upon the possibility to determine the $α_s$ from the $τ$--lepton width.

hep-ph↗

arXiv1995

Statistics of random quasi 1D Hamiltonian with slowly varying parameters. Painlevé again.

The statistics of random band--matrices with width and strength of the band slowly varying along the diagonal is considered. The Dyson equation for the averaged Green function close to the edge of spectrum is reduced to the Painlevé I equation. The analytical properties of the Green function allow to fix the solution of this equation. The former appears to be the same as that arose within the random--matrix regularization of 2d-gravity.

cond-mat↗

arXiv1994

Instanton--Antiinstanton pair induced Asymptotics of Perturbation Theory in QCD

The instanton--antiinstanton pair induced asymptotics of perturbation theory expansion for QCD correlators is considered. It is argued that though the true asymptotics is dominated by renormalon, the instanton-induced contribution may dominate in the intermediate asymptotics $n= 5÷15$. Obtained asymptotic formulae are valid for $N_f \le N_c$. For $N_f =N_c$ the finite nonperturbative expression for instanton--antiinstanton contribution was also found. At $q^2<0$ the imaginary part of correlators in the case $N_f =N_c$ is suppressed like $1/\log (q/Λ)$, but the present accuracy of instanton calculations allows to fix it unambiguously. The series of corrections to the instanton induced asymptotics of the order of $\sim (\log(n)/n)^k$ is found.

hep-ph↗

arXiv1994

Instanton -- Antiinstanton interaction and asymptotics of perturbation theory expansion in double well oscillator

Instanton -- antiinstanton pair is considered as a source of singularity at the Borel plane for the ground state energy of anharmonic oscillator. The problem of defining the short range instanton -- antiinstanton interaction reduces to calculation of a smooth part of the Borel function, which cannot be found without explicit calculation of several terms of ordinary perturbation theory. On the other hand, the large order terms of perturbative expansion are dominated by large fluctuations in the functional integral like well separated instanton and antiinstanton. The preasymptotics ($\sim 1/n$) of large order perturbation theory contribution to the ground state energy of anharmonic oscillator was found analytically. To this end the subleading long range asymptotics of the classical instanton -- antiinstanton interaction, the one -- loop quantum contribution to instanton -- antiinstanton interaction and the second quantum correction to a single instanton density were considered.

hep-ph↗

arXiv1992

Constrained Instanton and Baryon Number Non--Conservation at High Energies

Constrained Instanton and Baryon Number Non--Conservation at High Energies, P.G.Silvestrov, BUDKERINP 92--92. The total cross-section for baryon number violating processes at high energies is usually parametrized as $σ_{total}\propto\exp(\frac{4π}α F(\varepsilon))$, where $\varepsilon =\sqrt{s}/E_0 , \,\, E_0 = \sqrt{6} πm_w/α$. In the present paper the third nontrivial term of the expansion \[ F(\varepsilon)= -1+\frac{9}{8}\varepsilon^{4/3} -\frac{9}{16}\varepsilon^2 -\frac{9}{32} \left( \frac{m_h}{m_w}\right)^2 \varepsilon^{8/3}\log\left( \frac{1}{3\varepsilon}\left( \frac{2m_w}{γm_h}\right)^2 \right) + O(\varepsilon^{8/3}) \] is obtained.The unknown corrections to $F(\varepsilon)$ are expected to be of the order of $\varepsilon^{8/3}$, but have neither $(m_h/m_w)^2$, nor $\log(\varepsilon)$ enhancement. The total cross-section is extremely sensitive to the value of single Instanton action. The correction to Instanton action $\triangle S\sim (mρ)^4 \log(mρ)/g^2$ is found ($ρ$ is the Instanton radius). For sufficiently heavy Higgs boson the $ρ$ -dependent part of the Instanton action is changed drastically. In this case even the leading contribution to $F(\varepsilon)$, responsible for a growth of cross-section due to the multiple production of classical W-bosons, is changed: \[ F(\varepsilon)=-1+ \frac{9}{8}\left( \frac{2}{3} \right)^{2/3} \varepsilon^{4/3} +\ldots \,\, , \,\, \varepsilon\ll 1\ll \varepsilon \left( \frac{m_h}{m_w} \right)^{3/2} \,\, . \]

hep-ph↗