Abstract: We investigate the combined finite-size and thermo-magnetic effects on the properties of the quark matter, in the context of the two-flavored Nambu-Jona-Lasinio model. In particular, by using the mean-field approximation and the Schwinger proper time method in a toroidal topology with periodic or antiperiodic conditions, we evaluate the chiral phase transition, the constituent quark mass and the thermal and spatial susceptibilities under the change of the size, temperature and strength of external magnetic field. To take into account the inverse magnetic catalysis phenomenon, we make use of a recently proposed magnetized coupling constant. The findings suggest that the observables are strongly affected by the variation of the variables and also by the periodicity of the boundary conditions, with the final outcomes depending on the balance of these competing phenomena.

Abstract: In loop quantum cosmology (LQC) the big bang singularity is generically resolved by a big bounce. This feature holds even when modified quantization prescriptions of the Hamiltonian constraint are used such as in mLQC-I and mLQC-II. While the later describes an effective description qualitatively similar to that of standard LQC, the former describes an asymmetric evolution with an emergent Planckian de-Sitter pre-bounce phase even in the absence of a potential. We consider the potential relation of these canonically quantized non-singular models with effective actions based on a geometric description. We find a 3-parameter family of metric-affine f (R) theories which accurately approximate the effective dynamics of LQC and mLQC-II in all regimes and mLQC-I in the post-bounce phase. Two of the parameters are fixed by enforcing equivalence at the bounce, and the background evolution of the relevant observables can be fitted with only one free parameter. It is seen that the non-perturbative effects of these loop cosmologies are universally encoded by a logarithmic correction that only depends on the bounce curvature of the model. In addition, we find that the best fit value of the free parameter can be very approximately written in terms of fundamental parameters of the underlying quantum description for the three models. The values of the best fits can be written in terms of the bounce density in a simple manner, and the values for each model are related to one another by a proportionality relation involving only the Barbero-Immirzi parameter.

Abstract: In this paper, we analyze the quantum vacuum in a radiation-dominated and CPT -invariant universe by further imposing the quantum states to be ultraviolet regular i.e., satisfying the Hadamard/adiabatic condition. For scalar fields, this is enforced by constructing the vacuum via the states of low-energy proposal. For spin -12 fields, we extend this proposal for a FLRW spacetime and apply it for the radiation-dominated and CPT -invariant universe. We focus on minimizing the smeared energy density around the big bang and give strong evidence that the resulting states satisfy the Hadamard/adiabatic condition. These states are then self -consistent candidates as effective big bang quantum vacuum from the field theory perspective.

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).

Abstract: Recently, the ANITA collaboration announced the detection of new, unsettling upgoing Ultra-High-Energy (UHE) events. Understanding their origin is pressing to ensure success of the incoming UHE neutrino program. In this work, we study their internal consistency and the implications of the lack of similar events in IceCube. We introduce a generic, simple parametrization to study the compatibility between these two observatories in Standard Model-like and Beyond Standard Model scenarios: an incoming flux of particles that interact with Earth nucleons with cross section sigma, producing particle showers along with long-lived particles that decay with lifetime iota and generate a shower that explains ANITA observations. We find that the ANITA angular distribution imposes significant constraints, and when including null observations from IceCube only iota similar to 10(-3)-10(-2) s and sigma similar to 10(-33) -10(-32) cm(2) can explain the data. This hypothesis is testable with future IceCube data. Finally, we discuss a specific model that can realize this scenario. Our analysis highlights the importance of simultaneous observations by high-energy optical neutrino telescopes and new UHE radio detectors to uncover cosmogenic neutrinos or discover new physics.