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Jay, G., Arnault, P., & Debbasch, F. (2021). Dirac quantum walks with conserved angular momentum. Quantum Stud. Math. Found., 8, 419–430.
Abstract: A quantum walk (QW) simulating the flat (1+2)D Dirac equation on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group SO(3), but rather of its double cover SU(2), the QW can only be defined globally on an extended spacetime where the polar angle extends from 0 to 4 pi. The coupling of the QW with arbitrary electromagnetic fields is also presented. Finally, the cylindrical relativistic Landau levels of the Dirac equation are computed explicitly and simulated by the QW.
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Nzongani, U., Zylberman, J., Doncecchi, C. E., Perez, A., Debbasch, F., & Arnault, P. (2023). Quantum circuits for discrete-time quantum walks with position-dependent coin operator. Quantum Inf. Process., 22(7), 270–46pp.
Abstract: The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with n wires, each corresponding to one qubit, we encode 2(n) position states. The data necessary to define an arbitrary position-dependent coin operator is therefore exponential in n. Hence, the exponentiality will necessarily appear somewhere in our circuits. We first propose a circuit implementing the position-dependent coin operator, that is naive, in the sense that it has exponential depth and implements sequentially all appropriate position-dependent coin operators. We then propose a circuit that “transfers” all the depth into ancillae, yielding a final depth that is linear in n at the cost of an exponential number of ancillae. Themain idea of this linear-depth circuit is to implement in parallel all coin operators at the different positions. Reducing the depth exponentially at the cost of having an exponential number of ancillae is a goal which has already been achieved for the problem of loading classical data on a quantum circuit (Araujo in Sci Rep 11:6329, 2021) (notice that such a circuit can be used to load the initial state of the walker). Here, we achieve this goal for the problem of applying a position-dependent coin operator in a discrete-time quantum walk. Finally, we extend the result of Welch (New J Phys 16:033040, 2014) from position-dependent unitaries which are diagonal in the position basis to position-dependent 2 x 2-block-diagonal unitaries: indeed, we show that for a position dependence of the coin operator (the block-diagonal unitary) which is smooth enough, one can find an efficient quantum-circuit implementation approximating the coin operator up to an error epsilon (in terms of the spectral norm), the depth and size of which scale as O(1/epsilon). A typical application of the efficient implementation would be the quantum simulation of a relativistic spin-1/2 particle on a lattice, coupled to a smooth external gauge field; notice that recently, quantum spatial-search schemes have been developed which use gauge fields as the oracle, to mark the vertex to be found (Zylberman in Entropy 23:1441, 2021), (Fredon arXiv:2210.13920). A typical application of the linear-depth circuit would be when there is spatial noise on the coin operator (and hence a non-smooth dependence in the position).
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Fujita, Y., Rubio, B., & Gelletly, W. (2011). Spin-isospin excitations probed by strong, weak and electro-magnetic interactions. Prog. Part. Nucl. Phys., 66(3), 549–606.
Abstract: Gamow-Teller (GT) transitions are the most common weak interaction processes of spin-isospin (sigma tau) type in atomic nuclei. They are of interest not only in nuclear physics but also in astrophysics; they play an important role in supernovae explosions and nucleosynthesis. The direct study of weak decay processes, however, gives relatively limited information about GT transitions and the states excited via GT transitions (GT states); beta decay can only access states at excitation energies lower than the decay Q-value, and neutrino-induced reactions have very small cross-sections. However, one should note that beta decay has a direct access to the absolute GT transition strengths B(GT) from a study of half-lives, Q(beta)-values and branching ratios. They also provide information on GT transitions in nuclei far-from-stability. Studies of M1 gamma transitions provide similar information. In contrast, the complementary charge-exchange (CE) reactions, such as the (p, n) or ((3)He, t) reactions at intermediate beam energies and 0 degrees, can selectively excite GT states up to high excitation energies in the final nucleus. It has been found empirically that there is a close proportionality between the cross-sections at 0 degrees and the transition strengths B(GT) in these CE reactions. Therefore, CE reactions are useful tools to study the relative values of B(GT) strengths up to high excitation energies. In recent ((3)He, t) measurements, one order-of-magnitude improvement in the energy resolution has been achieved. This has made it possible to make one-to-one comparisons of GT transitions studied in CE reactions and beta decays. Thus GT strengths in ((3)He, t) reactions can be normalised by the beta-decay values. In addition, comparisons with closely related M1 transitions studied in gamma decay or electron inelastic scattering [(e, e')1, and furthermore with “spin” M I transitions that can be studied by proton inelastic scattering [(p, p')[ have now been made possible. In these comparisons, the isospin quantum number T and associated symmetry structure in the same mass A nuclei (isobars) play a key role. Isospin symmetry can extend our scope even to the structures of unstable nuclei that are far from reach at present unstable beam factories.
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Alvarez-Ruso, L. et al, & Nieves, J. (2018). NuSTEC White Paper: Status and challenges of neutrino-nucleus scattering. Prog. Part. Nucl. Phys., 100, 1–68.
Abstract: The precise measurement of neutrino properties is among the highest priorities in fundamental particle physics, involving many experiments worldwide. Since the experiments rely on the interactions of neutrinos with bound nucleons inside atomic nuclei, the planned advances in the scope and precision of these experiments require a commensurate effort in the understanding and modeling of the hadronic and nuclear physics of these interactions, which is incorporated as a nuclear model in neutrino event generators. This model is essential to every phase of experimental analyses and its theoretical uncertainties play an important role in interpreting every result. In this White Paper we discuss in detail the impact of neutrino-nucleus interactions, especially the nuclear effects, on the measurement of neutrino properties using the determination of oscillation parameters as a central example. After an Executive Summary and a concise Overview of the issues, we explain how the neutrino event generators work, what can be learned from electron-nucleus interactions and how each underlying physics process – from quasi-elastic to deep inelastic scattering – is understood today. We then emphasize how our understanding must improve to meet the demands of future experiments. With every topic we find that the challenges can be met only with the active support and collaboration among specialists in strong interactions and electroweak physics that include theorists and experimentalists from both the nuclear and high energy physics communities.
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PTOLEMY Collaboration(Betti, M. G. et al), de Salas, P. F., Gariazzo, S., & Pastor, S. (2019). A design for an electromagnetic filter for precision energy measurements at the tritium endpoint. Prog. Part. Nucl. Phys., 106, 120–131.
Abstract: We present a detailed description of the electromagnetic filter for the PTOLEMY project to directly detect the Cosmic Neutrino Background (CNB). Starting with an initial estimate for the orbital magnetic moment, the higher-order drift process of E x B is configured to balance the gradient-B drift motion of the electron in such a way as to guide the trajectory into the standing voltage potential along the mid-plane of the filter. As a function of drift distance along the length of the filter, the filter zooms in with exponentially increasing precision on the transverse velocity component of the electron kinetic energy. This yields a linear dimension for the total filter length that is exceptionally compact compared to previous techniques for electromagnetic filtering. The parallel velocity component of the electron kinetic energy oscillates in an electrostatic harmonic trap as the electron drifts along the length of the filter. An analysis of the phase-space volume conservation validates the expected behavior of the filter from the adiabatic invariance of the orbital magnetic moment and energy conservation following Liouville's theorem for Hamiltonian systems. (C) 2019 Elsevier B.V. All rights reserved.
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Davesne, D., Pastore, A., & Navarro, J. (2021). Linear response theory with finite-range interactions. Prog. Part. Nucl. Phys., 120, 103870–55pp.
Abstract: This review focuses on the calculation of infinite nuclear matter response functions using phenomenological finite-range interactions, equipped or not with tensor terms. These include Gogny and Nakada families, which are commonly used in the literature. Because of the finite-range, the main technical difficulty stems from the exchange terms of the particle-hole interaction. We first present results based on the so-called Landau and Landau-like approximations of the particle-hole interaction. Then, we review two methods which in principle provide numerically exact response functions. The first one is based on a multipolar expansion of both the particle-hole interaction and the particle-hole propagator and the second one consists in a continued fraction expansion of the response function. The numerical precision can be pushed to any degree of accuracy, but it is actually shown that two or three terms suffice to get converged results. Finally, we apply the formalism to the determination of possible finite-size instabilities induced by a finite-range interaction.
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Addazi, A. et al, Martinez-Mirave, P., Mitsou, V. A., Palomares-Ruiz, S., Tortola, M., & Zornoza, J. D. (2022). Quantum gravity phenomenology at the dawn of the multi-messenger era-A review. Prog. Part. Nucl. Phys., 125, 103948–119pp.
Abstract: The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review, prepared within the COST Action CA18108 “Quantum gravity phenomenology in the multi-messenger approach”, is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers.
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Albaladejo, M., Bibrzycki, L., Dawid, S. M., Fernandez-Ramirez, C., Gonzalez-Solis, S., Hiller Blin, A. N., et al. (2022). Novel approaches in hadron spectroscopy. Prog. Part. Nucl. Phys., 127, 103981–75pp.
Abstract: The last two decades have witnessed the discovery of a myriad of new and unexpected hadrons. The future holds more surprises for us, thanks to new-generation experiments. Understanding the signals and determining the properties of the states requires a parallel theoretical effort. To make full use of available and forthcoming data, a careful amplitude modeling is required, together with a sound treatment of the statistical uncertainties, and a systematic survey of the model dependencies. We review the contributions made by the Joint Physics Analysis Center to the field of hadron spectroscopy.
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Nieves, J., Feijoo, A., Albaladejo, M., & Du, M. L. (2024). Lowest-lying 1/2- and 3/2- ΛQ resonances: From the strange to the bottom sectors. Prog. Part. Nucl. Phys., 137, 104118–23pp.
Abstract: We present a detailed study of the lowest-lying 1/2(-) and 3/2(-) Lambda Q resonances both in the heavy 2 2 quark (bottom and charm) and the strange sectors. We have paid special attention to the interplay between the constituent quark-model and chiral baryon-meson degrees of freedom, which are coupled using a unitarized scheme consistent with leading-order heavy quark symmetries. We show that the Lambda(b)(5912) [J(P) = 1/2(-)], Lambda(b)(5920) [J(P) = 3/2(-)] and the Lambda(c)(2625) [J(P) = 3/2-], and the Lambda(1520) [J(P) = 3/2(-)] admitting larger breaking corrections, are heavyquark spin-flavor siblings. They can be seen as dressed quark-model states with Sigma Q(()*()) pi molecular components of the order of 30%. The J(P)=1(-) Lambda(2595) has, however, a higher molecular 2 probability of at least 50%, and even values greater than 70% can be easily accommodated. This is because it is located almost on top of the threshold of the Sigma(c)pi pair, which largely influences its properties. Although the light degrees of freedom in this resonance would be coupled to spin-parity 1(-) as in the Lambda(b)(5912), Lambda(b)(5920) and Lambda(c)(2625), the Lambda(c)(2595) should not be considered as a heavy-quark spin-flavor partner of the former ones. We also show that the Lambda(1405) chiral two-pole pattern does not have analogs in the 1 – charmed and bottomed sectors, because the 2 N D-(*()) and N (B) over bar (()*()) channels do not play for heavy quarks the decisive role that the N (K) over bar does in the strange sector, and the notable influence of the bare quark-model states for the charm and bottom resonances. Finally, we predict the existence of two Lambda(b)(6070) and two Lambda(c)(2765) heavy-quark spin and flavor sibling odd parity states.
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Casas, F., Oteo, J. A., & Ros, J. (2012). Unitary transformations depending on a small parameter. Proc. R. Soc. A, 468(2139), 685–700.
Abstract: We formulate a unitary perturbation theory for quantum mechanics inspired by the Lie-Deprit formulation of canonical transformations. The original Hamiltonian is converted into a solvable one by a transformation obtained through a Magnus expansion. This ensures unitarity at every order in a small parameter. A comparison with the standard perturbation theory is provided. We work out the scheme up to order ten with some simple examples.
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