Search

It is known that computing the permanent of the matrix $1+A$, where $A$ is a finite-rank matrix, requires a number of operations polynomial in the matrix size. Motivated by the boson-sampling proposal of restricted quantum computation, I extend this result to a generalization of the matrix permanent: an expectation value in a product of a large number of identical bosonic states with a bounded number of bosons. This result complements earlier studies on the computational complexity in boson sampling and related setups. The proposed technique based on the Gaussian averaging is equally applicable to bosonic and fermionic systems. This also allows us to improve an earlier polynomial complexity estimate for the fermionic version of the same problem., Comment: 4 pages, introduction and conclusion expanded, minor style corrections

Inclusive as well as exclusive emissions in forward and central directions of rapidity are widely recognized as excellent channels to access the proton structure at small-x. In this regime, to describe nucleons structure, it is necessary to use kT-unintegrated distributions. In particular, at large transverse momenta, the x-evolution of the so-called unintegrated gluon distribution is driven by the Balitsky-Fadin-Kuraev-Lipatov equation, within the framework of the high-energy factorization (HEF). Recent analyses on the diffractive electroproduction of \rho mesons have corroborated the underlying assumption that the small-size dipole scattering mechanism is at work, thus validating the use of the HEF formalism. Nonetheless, a significant sensitivity of polarized cross sections to intermediate values of the meson transverse momenta, where, in the case of inclusive emissions, a description at the hand of the transverse momentum dependent (TMD) factorization starts to be the most appropriate framework, has been observed. In this work, we will review the formal description of the UGD within the BFKL approach and present some UGD models that have been proposed, then we will describe the state of the art of some recent phenomenological analyses., Comment: 5 pages, 4 figures, contribution to the proceedings of the 19th International Conference on Hadron Spectroscopy and Structure in memoriam Simon Eidelman (HADRON2021)

The Ultraviolet Transient Astronomical Satellite is a scientific space mission carrying an astronomical telescope. The mission is led by the Weizmann Institute of Science in Israel and the Israel Space Agency, while the camera in the focal plane is designed and built by Deutsches Elektronen Synchrotron in Germany. Two key science goals of the mission are the detection of counterparts to gravitational wave sources and supernovae. The launch to geostationary orbit is planned for 2024. The telescope with a field-of-view of $\approx200$deg$^2$, is optimized to work in the near-ultraviolet band between $220$ and $280$nm. The focal plane array is composed of four $22.4$-megapixel, backside-illuminated CMOS sensors with a total active area of 90x90mm$^2$. Prior to sensor production, smaller test sensors have been tested to support critical design decisions for the final flight sensor. These test sensors share the design of epitaxial layer and anti-reflective coatings (ARC) with the flight sensors. Here, we present a characterization of these test sensors. Dark current and read noise are characterized as a function of the device temperature. A temperature-independent noise level is attributed to on-die infrared emission and the read-out electronics` self-heating. We utilize a high-precision photometric calibration setup to obtain the test sensors` quantum efficiency (QE) relative to PTB/NIST-calibrated transfer standards ($220$-$1100$nm), the quantum yield for $\lambda < 300$nm, the non-linearity of the system, and the conversion gain. The uncertainties are discussed in the context of the newest results on the setup`s performance parameters. From three ARC options, Tstd, T1 and T2, the latter optimizes out-of-band rejection and peaks in the mid of the ULTRASAT operational waveband (max. QE $\approx80\%$ at $245\mathrm{nm}$). We recommend ARC option T2 for the final ULTRASAT UV sensor.

The Ultraviolet Transient Astronomical Satellite (ULTRASAT) is a scientific UV space telescope that will operate in geostationary orbit. The mission, targeted to launch in 2024, is led by the Weizmann Institute of Science (WIS) in Israel and the Israel Space Agency (ISA). Deutsches Elektronen Synchrotron (DESY) in Germany is tasked with the development of the UV-sensitive camera at the heart of the telescope. The camera's total sensitive area of ~90mm x 90mm is built up by four back-side illuminated CMOS sensors, which image a field of view of ~200 deg2. Each sensor has 22.4 megapixels. The Schmidt design of the telescope locates the detector inside the optical path, limiting the overall size of the assembly. As a result, the readout electronics is located in a remote unit outside the telescope. The short focal length of the telescope requires an accurate positioning of the sensors within +-50 mu along the optical axis, with a flatness of +-10 mu. While the telescope will be at around 295K during operations, the sensors are required to be cooled to 200K for dark current reduction. At the same time, the ability to heat the sensors to 343K is required for decontamination. In this paper, we present the preliminary design of the UV sensitive ULTRASAT camera., Comment: "UV, X-Ray, and Gamma-Ray Space Instrumentation for Astronomy XXII", Proc. SPIE 11821, Optics and Photonics, 11821-21 (August, 2021). Contact authors Rolf Buehler (rolf.buehler@desy.de) and Merlin Barschke (merlin.barschke@desy.de)

We study the computational complexity of quantum-mechanical expectation values of single-particle operators in bosonic and fermionic multi-particle product states. Such expectation values appear, in particular, in full-counting-statistics problems. Depending on the initial multi-particle product state, the expectation values may be either easy to compute (the required number of operations scales polynomially with the particle number) or hard to compute (at least as hard as a permanent of a matrix). However, if we only consider full counting statistics in a finite number of final single-particle states, then the full-counting-statistics generating function becomes easy to compute in all the analyzed cases. We prove the latter statement for the general case of the fermionic product state and for the single-boson product state (the same as used in the boson-sampling proposal). This result may be relevant for using multi-particle product states as a resource for quantum computing., Comment: 8 pages, published version

We propose to investigate the full counting statistics of nonequilibrium spin transport with an ultracold atomic quantum gas. The setup makes use of the spin control available in atomic systems to generate spin transport induced by an impurity atom immersed in a spin-imbalanced two-component Fermi gas. In contrast to solid-state realizations, in ultracold atoms spin relaxation and the decoherence from external sources is largely suppressed. As a consequence, once the spin current is turned off by manipulating the internal spin degrees of freedom of the Fermi system, the nonequilibrium spin population remains constant. Thus one can directly count the number of spins in each reservoir to investigate the full counting statistics of spin flips, which is notoriously challenging in solid state devices. Moreover, using Ramsey interferometry, the dynamical impurity response can be measured. Since the impurity interacts with a many-body environment that is out of equilibrium, our setup provides a way to realize the non-equilibrium orthogonality catastrophe. Here, even for spin reservoirs initially prepared in a zero-temperature state, the Ramsey response exhibits an exponential decay, which is in contrast to the conventional power-law decay of Anderson's orthogonality catastrophe. By mapping our system to a multi-step Fermi sea, we are able to derive analytical expressions for the impurity response at late times. This allows us to reveal an intimate connection of the decay rate of the Ramsey contrast and the full counting statistics of spin flips., Comment: 9+11 pages, 10 figures

Ultra-High Energy Cosmic Rays (UHECRs) are charged particles of energies above $10^{18}$ eV that originate outside of the Galaxy. Because the flux of the UHECRs at Earth is very small, the only practical way of observing UHECRs is by measuring the extensive air showers (EAS) produced by UHECRs in the atmosphere. This is done by using air fluorescence detectors and giant arrays of particle detectors on the ground. The Pierre Auger Observatory (Auger) and Telescope Array (TA) are two large cosmic ray experiments which use such techniques and cover 3000 km$^2$ and 700 km$^2$ areas on the ground, respectively. In this paper, we present the UHECR spectrum reported by the TA, using an exposure of 6300 km$^2$ sr yr accumulated over 7 years of data taking, and the corresponding result of Auger, using 10 years of data with a total exposure exceeding 50000 km$^2$ sr yr. We review the astrophysical interpretation of the two measurements, and discuss their systematic uncertainties., Comment: 31 pages, 19 figures, accepted for publication in Prog. Theor. Exp. Phys

In this work we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate and prove that within the considered model the fastest rate of long-time decoherence is given by $\gamma=\pi k_BT/4$. We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures $T/T_F\lesssim 0.2$ where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid $^3$He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several phenomena that can be tested using currently available experimental technology., Comment: 27+16 pages, 21 figures; final version

Noninteracting bosons were proposed to be used for a demonstration of quantum-computing supremacy in a boson-sampling setup. A similar demonstration with fermions would require that the fermions are initially prepared in an entangled state. I suggest that pairwise entanglement of fermions would be sufficient for this purpose. Namely, it is shown that computing multi-particle scattering amplitudes for fermions entangled pairwise in groups of four single-particle states is #P hard. In linear algebra, such amplitudes are expressed as exterior products of two-forms of rank two. In particular, a permanent of a NxN matrix may be expressed as an exterior product of N^2 two-forms of rank two in dimension 2N^2, which establishes the #P-hardness of the latter., Comment: 5 pages, version accepted for publication

We revisit the problem of full counting statistics of particles on a segment of a one-dimensional gas of free fermions. Using a combination of analytical and numerical methods, we study the crossover between the counting of discrete particles and of the continuous particle density as a function of smoothing in the counting procedure. In the discrete-particle limit, the result is given by the Fisher--Hartwig expansion for Toeplitz determinants, while in the continuous limit we recover the bosonization results. This example of full counting statistics with smoothing is also related to orthogonality catastrophe, Fermi-edge singularity and non-equilibrium bosonization., Comment: 7 pages, 4 figures

Motivated by the recent results on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities, we develop an asymptotic expansion for transverse spin correlations in the XX spin-1/2 chain. The coefficients of the expansion can be calculated to any given order using the relation to discrete Painleve equations. We present explicit results up to eleventh order and compare them with a numerical example., Comment: 7 pages

One of several working groups established for this workshop was charged with examining results and methods associated with the UHECR energy spectrum. We summarize the results of our discussions, which include a better understanding of the analysis choices made by groups and their motivation. We find that the energy spectra determined by the larger experiments are consistent in normalization and shape after energy scaling factors are applied. Those scaling factors are within systematic uncertainties in the energy scale, and we discuss future work aimed at reducing these systematics., Comment: Working Group report given at UHECR 2012 Symposium, CERN, Feb. 2012

We study the spectrum of the Toeplitz matrix with a sine kernel, which corresponds to the single-particle reduced density matrix for free fermions on the one-dimensional lattice. For the spectral determinant of this matrix, a Fisher--Hartwig expansion in the inverse matrix size has been recently conjectured. This expansion can be verified order by order, away from the line of accumulation of zeros, using the recurrence relation known from the theory of discrete Painleve equations. We perform such a verification to the tenth order and calculate the corresponding coefficients in the Fisher-Hartwig expansion. Under the assumption of the validity of the Fisher-Hartwig expansion in the whole range of the spectral parameter, we further derive expansions for an equation on the eigenvalues of this matrix and for the von Neumann entanglement entropy in the corresponding fermion problem. These analytical results are supported by a numerical example., Comment: 10 pages, minor typos corrected, corresponds to published version

We consider the entanglement entropy for a line segment in the system of noninteracting one-dimensional fermions at zero temperature. In the limit of a large segment length L, the leading asymptotic behavior of this entropy is known to be logarithmic in L. We study finite-size corrections to this asymptotic behavior. Based on an earlier conjecture of the asymptotic expansion for full counting statistics in the same system, we derive a full asymptotic expansion for the von Neumann entropy and obtain first several corrections for the Renyi entropies. Our corrections for the Renyi entropies reproduce earlier results. We also discuss the entanglement spectrum in this problem in terms of single-particle occupation numbers., Comment: 6 pages, comparison with numerics added, published version

We propose to describe correlations in classical and quantum systems in terms of full counting statistics of a suitably chosen discrete observable. The method is illustrated with two exactly solvable examples: the classical one-dimensional Ising model and the quantum spin-1/2 XY chain. For the one-dimensional Ising model, our method results in a phase diagram with two phases distinguishable by the long-distance behavior of the Jordan-Wigner strings. For the quantum XY chain, the method reproduces the previously known phase diagram., Comment: 6 pages, section on Lee-Yang zeros added, published version

We derive an asymptotic expansion for a Wiener-Hopf determinant arising in the problem of counting one-dimensional free fermions on a line segment at zero temperature. This expansion is an extension of the result in the theory of Toeplitz and Wiener-Hopf determinants known as the generalized Fisher-Hartwig conjecture. The coefficients of this expansion are conjectured to obey certain periodicity relations, which renders the expansion explicitly periodic in the "counting parameter". We present two methods to calculate these coefficients and verify the periodicity relations order by order: the matrix Riemann-Hilbert problem and the Painleve V equation. We show that the expansion coefficients are polynomials in the counting parameter and list explicitly first several coefficients., Comment: 11 pages, minor corrections, published version

We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating function for this probability distribution can be expressed as a determinant of a Toeplitz matrix. We use the recently proven generalized Fisher--Hartwig conjecture on the asymptotic behavior of such determinants to find the generating function for the full counting statistics of fermions on a line segment. Unlike the method of bosonization, the Fisher--Hartwig formula correctly takes into account the discreteness of charge. Furthermore, we check numerically the precision of the generalized Fisher--Hartwig formula, find that it has a higher precision than rigorously proven so far, and conjecture the form of the next-order correction to the existing formula., Comment: 17 pages, 2 figures, Latex, iopart.cls

We propose a new quantum model interpolating between the fully frustrated spin-1/2 Ising model in a transverse field and a dimer model. This model contains a resonating-valence-bond phase, including a line with an exactly solvable ground state of the Rokhsar-Kivelson type. We discuss the phase diagrams of this model on the square and triangular (in terms of the dimer representation) lattices., Comment: 9 pages, 7 figures

We study vison excitations in a quantum dimer model interpolating between the Rokhsar-Kivelson models on the square and triangular lattices. In the square-lattice case, the model is known to be critical and characterized by U(1) topological quantum numbers. Introducing diagonal dimers brings the model to a Z_2 resonating-valence-bond phase. We study variationally the emergence of vison excitations at low concentration of diagonal dimers, close to the critical point. We find that, in this regime, vison excitations are large in size and their structure resembles vortices in type-II superconductors., Comment: 6 pages, 2 figures, minor corrections corresponding to the published version

We discuss the problem of full counting statistics for periodic pumping. The probability generating function is usually defined on a circle of the "physical" values of the counting parameter, with its periodicity corresponding to charge quantization. The extensive part of the generating function can either be an analytic function on this circle or have singularities. These two cases may be interpreted as different thermodynamic phases in time domain. We discuss several examples of phase transitions between these phases for classical and quantum systems. Finally, we prove a criterion for the "analytic" phase in the problem of a quantum pump for noninteracting fermions., Comment: 5 pages, 4 figures

We use an SU(2) mean-field theory approach with input from variational wavefunctions of the t-J model to study the electronic spectra in the pseudogap phase of cuprates. In our model, the high-temperature state of underdoped cuprates is realized by classical fluctuations of the order parameter between the d-wave superconductor and the staggered-flux state. Spectral functions of the intermediate and the averaged states are computed and analyzed. Our model predicts a photoemission spectrum with an asymmetric gap structure interpolating between the superconducting gap centered at the Fermi energy and the asymmetric staggered-flux gap. This asymmetry of the gap changes sign at the point where the Fermi surface crosses the diagonal (\pi,0)-(0,\pi)., Comment: 7 pages, 10 figures; estimate of applicable temperature range corrected and refs. added, ref. to ARPES paper added; minor changes to published version

We consider the doped Rokhsar-Kivelson quantum dimer model on the triangular lattice with one mobile hole (monomer) at the Rokhsar-Kivelson point. The motion of the hole is described by two branches of excitations: the hole may either move with or without a trapped Z2 vortex (vison). We perform a study of the hole dispersion in the limit where the hole hopping amplitude is much smaller than the interdimer interaction. In this limit, the hole without vison moves freely and has a tight-binding spectrum. On the other hand, the hole with a trapped vison is strongly constrained due to interference effects and can only move via higher-order virtual processes., Comment: 4 pages, 4 figures; minor changes, replaced by published version

We show that the liquid-to-crystal quantum phase transition in the Rokhsar--Kivelson dimer model on the two-dimensional triangular lattice occurs as a condensation of vortex-like excitations called ``visons''. This conclusion is drawn from the numerical studies of the vison spectrum in the liquid phase by using the Green's function Monte Carlo method. We find that visons remain the lowest excitation throughout the liquid phase and that their gap decreases continuously to zero at the phase transition. The nature of the crystal phase and the second order of the phase transition are in agreement with the earlier prediction of Moessner and Sondhi [Phys. Rev. B 63, 224401 (2001)]., Comment: 4 pages, 4 figures

We analyze the electronic Green's functions in the superconducting ground state of the t-J model using Gutzwiller-projected wave functions, and compare them to the conventional BCS form. Some of the properties of the BCS state are preserved by the projection: the total spectral weight is continuous around the quasiparticle node and approximately constant along the Fermi surface. On the other hand, the overall spectral weight is reduced by the projection with a momentum-dependent renormalization, and the projection produces electron-hole asymmetry in renormalization of the electron and hole spectral weights. The latter asymmetry leads to the bending of the effective Fermi surface which we define as the locus of equal electron and hole spectral weight., Comment: 7 pages, 3 figures, Proceedings of the "11th Training Course in the Physics of Strongly Correlated Systems and high Tc Superconductors", Vietri sul Mare, Salerno, Italy, Oct. 2006

The amplitude for the forward electroproduction of two light vector mesons can be written completely within perturbative QCD in the Regge limit with next-to-leading accuracy, thus providing the first example of a physical application of the BFKL approach at the next-to-leading order. Recently, a numerical determination of the amplitude has been obtained in the case of equal photon virtualities, by using a definite representation for the amplitude and a definite optimization method for the perturbative series. Here, we study the main systematic effects in the previous determination, by considering a different representation of the amplitude and different optimization methods of the perturbative series. Moreover, we compare our result for the differential cross section at the minimum $|t|$ with a different approach, based on collinear kernel improvement., Comment: 7 pages, 4 figures; proceedings of DIFFRACTION 2006, Workshop on Diffraction in High-Energy Physics, Milos (Greece), Sep. 5-10, 2006

We analyze the electronic Green's functions in the superconducting ground state of the t-J model using Gutzwiller-projected wave functions, and compare them to the conventional BCS form. Some of the properties of the BCS state are preserved by the projection: the total spectral weight is continuous around the quasiparticle node and approximately constant along the Fermi surface. On the other hand, the overall spectral weight is reduced by the projection with a momentum-dependent renormalization, and the projection produces electron-hole asymmetry in renormalization of the electron and hole spectral weights. The latter asymmetry leads to the bending of the effective Fermi surface which we define as the locus of equal electron and hole spectral weight., Comment: 6 pages, 5 figures; x-labels on Figs. 1 and 2 corrected, footnote on particle number corrected, references added

We report on an exhaustive investigation of the dynamical dimer-dimer correlations in imaginary time for the quantum dimer model on the triangular lattice using the Green's function Monte Carlo method. We show in particular that soft modes develop upon reducing the dimer-dimer repulsion, indicating the presence of a second-order phase transition into an ordered phase with broken translational symmetry. We further investigate the nature of this ordered phase, for which a 12-site unit cell has been previously proposed, with the surprising result that significant Bragg peaks are only present at two of the three high-symmetry points consistent with this unit cell. We attribute the absence of a detectable peak to its small magnitude due to the nearly uniform internal structure of the 12-site crystal cell., Comment: 6 pages, 8 figures

With the use of Gutzwiller-projected variational states, we study the renormalization of the current carried by the quasiparticles in high-temperature superconductors and of the quasiparticle spectral weight. The renormalization coefficients are computed by the variational Monte Carlo technique, under the assumption that quasiparticle excitations may be described by Gutzwiller-projected BCS quasiparticles. We find that the current renormalization coefficient decreases with decreasing doping and tends to zero at zero doping. The quasiparticle spectral weight Z_+ for adding an electron shows an interesting structure in k space, which corresponds to a depression of the occupation number k just outside the Fermi surface. The perturbative corrections to those quantities in the Hubbard model are also discussed., Comment: 9 pages, 9 figures

Using exact diagonalizations and Green's function Monte Carlo simulations, we have studied the zero-temperature properties of the quantum dimer model on the triangular lattice on clusters with up to 588 sites. A detailed comparison of the properties in different topological sectors as a function of the cluster size and for different cluster shapes has allowed us to identify different phases, to show explicitly the presence of topological degeneracy in a phase close to the Rokhsar-Kivelson point, and to understand finite-size effects inside this phase. The nature of the various phases has been further investigated by calculating dimer-dimer correlation functions. The present results confirm and complement the phase diagram proposed by Moessner and Sondhi on the basis of finite-temperature simulations [Phys. Rev. Lett. {\bf 86}, 1881 (2001)]., Comment: 10 pages, 16 figures

We have studied in perturbative QCD all independent helicity amplitudes describing the photoproduction of light vector mesons at large $t$. We found a new hard production mechanism which is related to the possibility for a real photon to fluctuate into a massless $q\bar q$ pair in a chiral-odd spin configuration. Each helicity amplitude is given as a sum of chiral-even contribution (when the helicities of quark and antiquark are antiparallel) and this additional chiral-odd part (where the helicities of quark and antiquark are parallel). The chiral-odd contribution is large, it leads to a dominance of the non spin-flip amplitude in a very broad region of intermediately high $|t|$.}, Comment: 3 pages, uses sprocl.sty, talk given at the DIS2000 conference, Liverpool, England, April 2000, to appear in the conference proceedings

Using impact-factor representation, we consider the lepton pair production by an incident high-energy photon in a strong electromagnetic field of a nucleus. By summing leading terms of perturbation series, we obtain a simple formula for the amplitude, valid to all orders in ${\cal O}(\alpha Z)$ and arbitrary field of the nucleus. Using these results, we derive, in a simple manner, the results for the lepton pair production by a virtual incident photon in a Coulomb field. For real incident photon our results coincide with the known ones. Also, a particular example of a non-Coulomb potential is discussed in some detail., Comment: 20 pages, Latex, 2 Figures

We present a low-energy effective model for the charge degrees of freedom in two-leg t-J ladders. Starting from SU(2) mean-field theory, we exclude the spin degrees of freedom which have an energy gap. At low temperatures, the mean-field solution is the staggered-flux phase. For gapless charge excitations the effective theory is the Luther-Emery liquid. Our analysis is applicable at low doping and in the ``physical'' range of parameters $t/J\sim 3$ where there is only one massless mode in the charge sector and no massless modes in the spin sector. Within our model we make predictions about correlation exponents and the superconductivity order parameter, and discuss the comparison with the existing numerical results., Comment: ReVTeX, 14 pages, 11 figures, uses epsf