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The uncertainty principle is one of the fundamental features of quantum mechanics and plays a vital role in quantum information processing. We study uncertainty relations based on metric-adjusted skew information for finite quantum observables. Motivated by the paper [Physical Review A 104, 052414 (2021)], we establish tighter uncertainty relations in terms of different norm inequalities. Naturally, we generalize the method to uncertainty relations of metric-adjusted skew information for quantum channels and unitary operators. As both the Wigner-Yanase-Dyson skew information and the quantum Fisher information are the special cases of the metric-adjusted skew information corresponding to different Morozova-Chentsov functions, our results generalize some existing uncertainty relations. Detailed examples are given to illustrate the advantages of our methods., Comment: 14 pages, 3 figures

The K-matrix approach is mostly used when analyzing the overlapping resonances. It provides unitarity of the scattering matrix, however, its parameters are not physical quantities; the resonant and background contributions cannot be separated; and the scattering amplitudes have zeros between the positions of resonances. The parameters of the Breit—Wigner (BW) functions are the masses and widths of resonances; however, the sum of such functions violates unitarity. We construct a unitary S-matrix by taking into account the interference of BW functions. In the examples presented in the paper, these two approaches are compared.

We study the gravity-mediated scattering of scalar fields based on a parameterisation of the Lorentzian quantum effective action. We demonstrate that the interplay of infinite towers of spin zero and spin two poles at imaginary squared momentum leads to scattering amplitudes that are compatible with unitarity bounds, causal, and scale-free at trans-Planckian energy. Our construction avoids introducing non-localities or the massive higher-spin particles that are characteristic in string theory., v2: various small improvements/clarifications, version accepted for publication

We present the theoretical considerations for the case of looking into a generalization of quantum theory corresponding to having an inner product with an indefinite signature on the Hilbert space. The latter is essentially a direct analog of having the Minkowski spacetime with an indefinite signature generalizing the metric geometry of the Newtonian space. In fact, the explicit physics setting we have in mind is exactly a Lorentz covariant formulation of quantum mechanics, which has been discussed in the literature for over half a century yet without a nice full picture. From the point of view of the Lorentz symmetry, indefiniteness of the norm for a Minkowski vector may be the exact correspondence of the indefiniteness of the norm for a quantum state vector on the relevant Hilbert space. That, of course, poses a challenge to the usual requirement of unitarity. The related issues will be addressed.

Despite being created through a fundamentally quantum-mechanical process, cosmological structures have not yet revealed any sign of genuine quantum correlations. Among the obstructions to the direct detection of quantum signatures in cosmology, environmental-induced decoherence is arguably one of the most inevitable. Yet, we discover a mechanism of quantum recoherence for the adiabatic perturbations when they couple to an entropic sector. After a transient phase of decoherence, a turning point is reached, recoherence proceeds and adiabatic perturbations exhibit a large amount of self-coherence at late-time. This result is also understood by means of a non-Markovian master equation, which reduces to Wilsonian effective-field theory in the unitary limit. This allows us to critically assess the validity of open-quantum-system methods in cosmology and to highlight that re(de)coherence from linear interactions has no flat-space analogue., Comment: 5 + 12 pages, 4 + 2 figures, matches published version in EPL

We elucidate universal many-body properties of a one-dimensional, two-component ultracold Fermi gas near the $p$-wave Feshbach resonance. The low-energy scattering in this system can be characterized by two parameters, that is, $p$-wave scattering length and effective range. At the unitarity limit where the $p$-wave scattering length diverges and the effective range is reduced to zero without conflicting with the causality bound, the system obeys universal thermodynamics as observed in a unitary Fermi gas with contact $s$-wave interaction in three dimensions. It is in contrast to a Fermi gas with the $p$-wave resonance in three dimensions in which the effective range is inevitably finite. We present the universal equation of state in this unitary $p$-wave Fermi gas within the many-body $T$-matrix approach as well as the virial expansion method. Moreover, we examine the single-particle spectral function in the high-density regime where the virial expansion is no longer valid. On the basis of the Hartree-like self-energy shift at the divergent scattering length, we conjecture that the equivalence of the Bertsch parameter across spatial dimensions holds even for a one-dimensional unitary $p$-wave Fermi gas., 9 pages, 5 figures

The frequencies of the analytic normal modes for N identical particles are studied as a function of system parameters from the weakly interacting BCS regime to the strongly interacting unitary regime. The normal modes were obtained previously from a first-order L=0 group theoretic solution of a three-dimensional Hamiltonian with a general two-body interaction for confined, identical particles. In a precursor to this study, the collective behavior of these normal modes was investigated as a function of N from few-body systems to many-body systems analyzing the contribution of individual particles to the collective macroscopic motions. A specific case, the Hamiltonian for Fermi gases in the unitary regime was studied in more detail. This regime is known to support collective behavior in the form of superfluidity and has previously been successfully described using normal modes. Two phenomena that could sustain the emergence and stability of superfluid behavior were revealed, including the behavior of the normal mode frequencies as N increases. In this paper, I focus on a more detailed analysis of these analytic frequencies, extending my investigation to include Hamiltonians with a range of interparticle interaction strengths from the BCS regime to the unitary regime and analyzing the microscopic dynamics that lead to large gaps at unitarity. The results of the current study suggest that in regimes where higher-order effects are small, normal modes an be used to describe the physics of superfluidity from the weakly interacting BCS regime with the emergence of small excitation gaps to unitarity with its large gaps, and can offer insight into a possible microscopic understanding of the behavior at unitarity. This approach could thus offer an alternative to the two-body pairing models commonly used to describe superfluidity along this transition., 23 pages including 7 Appendices and 16 figures

We present a method for calculating the time-dependent many-body wavefunction that follows a local quench. We apply the method to the voltage-driven nonequilibrium Kondo model to find the exact time-evolving wavefunction following a quench where the dot is suddenly attached to the leads at $t=0$. The method, which does not use Bethe ansatz, also works in other quantum impurity models (we include results for the interacting resonant level and the Anderson impurity model) and may be of wider applicability. In the particular case of the Kondo model, we show that the long-time limit (with the system size taken to infinity first) of the time-evolving wavefunction is a current-carrying nonequilibrium steady state that satisfies the Lippmann-Schwinger equation. We show that the electric current in the time-evolving wavefunction is given by a series expression that can be expanded either in weak coupling or in strong coupling, converging to all orders in the steady-state limit in either case. The series agrees to leading order with known results in the well-studied regime of weak antiferromagnetic coupling and also reveals another universal regime of strong ferromagnetic coupling, with Kondo temperature $T_K^{(F)} = D e^{-\frac{3\pi^2}{8} \rho |J|}$ ($J, Comment: 6 pages (main text 5 pages). Published version. arXiv admin note: substantial text overlap with arXiv:1912.00281

We comment on phase selection of the scattering amplitude, emphasizing that the elastic overlap function should have a central impact parameter profile at high energies and highlighting the role of the reflective scattering mode at the LHC energies. Emerging problems with the use of peripheral impact parameter dependence of the elastic overlap function are explicitly indicated. Their solution is an elimination of the phases connected to peripheral form of the elastic overlap function. Contrary, we adhere to a relative peripheral form of the {\it inelastic} overlap function with an additional new feature of a maximum at nonzero value of the impact parameter at the highest energies. Phenomenologically, the dynamics of hadron scattering is motivated by a hadron structure with a hard central core presence., Comment: 13 pages, 2 figures, revised version

A new simple qubit model of black hole evaporation is proposed. The model operates on four qubits and is defined in terms of quantum gates and a quantum circuit. The chief features of the model include explicit unitarity and (most notably) causality which is understood as the impossibility of the transfer of information from the interior of the black hole through its horizon. The corresponding von Neumann entanglement entropy yields a crude (four-qubit) approximation of the Page curve., 8 pages, 3 figures (including 8 pictures), minor editorial improvements in this version

By including the effect of a trap with characteristic energy given by the Fermi temperature T F in a two-body two-channel model for Feshbach resonances, we reproduce the measured binding energy of ultracold molecules in a 40K atomic Fermi gas. We also reproduce the experimental closed-channel fraction Z across the BEC–BCS crossover and into the BCS regime of a 6Li atomic Fermi gas. We obtain the expected behavior Z ∝ T F at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the Z dependency on T F on the BCS side, where a significant quantitative discrepancy between experimental data and theory’s predictions has been repeatedly reported. In order to contrast with future experiments we report the proportionality constant at unitarity between Z and T F predicted by our model for a 40K atomic Fermi gas.

Having both elastic and inelastic two-body processes that are characterized by a complex $s$-wave scattering length between $\uparrow$ and $\downarrow$ fermions in mind, here we apply the non-Hermitian extension of the mean-field theory to the BCS-BEC evolution at zero temperature. We construct the phase diagram of the system, where we find a reentrant superfluid (SF) transition that is intervened by a normal and/or a metastable phase as a function of increasing inelasticity. This transition occurs in a large parameter regime away from the unitarity, i.e., both on the BCS and BEC sides of the resonance, and it is mostly governed by the exceptional points. In addition, except for the strongly-inelastic regime, we also show that the SF phase can be well-described by the condensation of weakly-interacting bosonic pairs in the two-body bound state with a complex binding energy., Comment: 6 pages with 3 figures

We discuss second quantization, discrete symmetry transformations and inner products in free non-Hermitian scalar quantum field theories with PT symmetry, focusing on a prototype model of two complex scalar fields with anti-Hermitian mass mixing. Whereas the definition of the inner product is unique for theories described by Hermitian Hamiltonians, its formulation is not unique for non-Hermitian Hamiltonians. Energy eigenstates are not orthogonal with respect to the conventional Dirac inner product, so we must consider additional discrete transformations to define a positive-definite norm. We clarify the relationship between canonical-conjugate operators and introduce the additional discrete symmetry C', previously introduced for quantum-mechanical systems, and show that the C'PT inner product does yield a positive-definite norm, and hence is appropriate for defining the Fock space in non-Hermitian models with PT symmetry in terms of energy eigenstates. We also discuss similarity transformations between PT-symmetric non-Hermitian scalar quantum field theories and Hermitian theories, showing that they would require modification in the presence of interactions. As an illustration of our discussion, we compare particle mixing in a Hermitian theory and in the corresponding non-Hermitian model with PT symmetry, showing how the latter maintains unitarity and exhibits mixing between scalar and pseudoscalar bosons., Comment: 44 pages, revtex format; to match published version, including a revised discussion of particle mixing and oscillations

We present that, if unitarizing the B(*)B(*) scattering amplitudes in the constituent interchange model, one can find two bound-state poles for (Itot,Stot)=(0,1) BB* and B*B* system, which correspond to two I(JP)=0(1+) doubly bottomed molecular states. Furthermore, it is noticed that the virtual states in (1,0) BB, (1,1) BB*, (1,0) B*B*, and (1,2) B*B* systems could produce enhancements of the squared moduli of the scattering T matrix just above the related thresholds, which might correspond to I(JP)=1(0+), 1(1+), and 1(2+) doubly bottomed molecular states, respectively. The calculation may be helpful for searching for the doubly bottomed molecular state in future experiments.

We study the CP domain walls and the consequent gravitational waves induced by the spontaneous breaking of the CP symmetry in the complex singlet extension to the Standard Model. We impose the constraints from the unitarity, stability and the global minimal of the vacuum solutions on the model parameter space. The CP domain wall profiles and tensions are obtained by numerically solving the relevant field equations. The explicit CP violation terms are then introduced to the potential as biased terms to make the domain walls unstable and collapse, The BBN bound on the magnitude of the energy bias is taken into account. To achieve sufficiently strong gravitational wave signals, the domain wall tension $\sigma$ is required to be at least $\sigma/{\rm TeV}^3 \sim \mathcal{O}(10^3)$. We find that the gravitational wave spectrum can be probed in the future SKA and/or DECIGO programs, when the typical mass scale is at least $\sim \mathcal{O}(10)$ TeV and the explicit CP violation terms are as small as $\mathcal{O}(10^{-29}) - \mathcal{O}(10^{-27}) $. The gravitational waves from collapsing domain walls thus provide a complementarity to the probe of extremely small CP violation at high-energy scale., Comment: 21 pages, 4 figures

Interaction of dipolar polaritons can be efficiently tuned by means of a shape resonance in their excitonic component. Provided the resonance width is large, a squeezed population of strongly interacting polaritons may persist on the repulsive side of the resonance. We derive an analytical expression for the polariton coupling constant and show that it may have very large values in typical experimental conditions. Our arguments provide a new direction for the quest of interactions in quantum photonics., 5 pages, 1 figure + Supplemental information

We give a detailed account of a stationary impurity in an ideal Bose-Einstein condensate, which we call the ideal Bose polaron, at both zero and non-zero temperatures and arbitrary strength of the impurity-boson coupling. The time evolution is solved exactly and it is found that, surprisingly, many of the features that have been predicted for the real BEC are already present in this simpler setting and can be understood analytically therein. We obtain explicit formulae for the time evolution of the condensate wave function at $T=0$ and of the one-particle density matrix at $T>0$. For negative scattering length, the system is found to thermalize even though the dynamics are perfectly coherent. The time evolution and thermal values of the Tan contact are derived and compared to a recent experiment. We find that contrary to the Fermi polaron, the contact is not bounded at unitarity as long as a condensate exists. An explicit formula for the dynamical overlap at $T=0$ allows us to compute the rf spectrum which can be understood in detail by relating it to the two-body problem of one boson and the impurity., 13 pages, 3 figures

High temperature virial expansion is a powerful tool in equilibrium statistical mechanics. In this letter we generalize the high temperature virial expansion approach to treat far-from-equilibrium quench dynamics. As an application of our framework, we study the dynamics of a Bose gas quenched from non-interacting to unitarity, and we compare our theoretical results with unexplained experimental results by the Cambridge group [Eigen et al., Nature 563, 221 (2018)]. We show that, during the quench dynamics, the momentum distribution decreases for low-momentum part with $kk^*$, where $k^*$ is a characteristic momentum scale separating the low- and the high-momentum regimes. We determine the universal value of $k^*\lambda$ that agrees perfectly with the experiment, with $\lambda$ being the thermal de Broglie wave length. We also find a jump of the half-way relaxation time across $k^*\lambda$ and the non-monotonic behavior of energy distribution, both of which agree with the experiment. Finally, we address the issue whether the long-time steady state thermalizes or not, and we find that this state does thermalize except for the very high momentum tail with $k\lambda\gg 1$. Our framework can also be applied to quench dynamics in other systems., Comment: 6 pages, 4 figures

By using an analytical exact non-Hermitian formalism for quantum tunneling decay that involves the expansion of the decaying wave function as a linear combination of resonant states and transient functions associated with the complex poles of the outgoing Green’s function to the problem, it is shown that the integrated decaying probability density in the whole space satisfies unitarity at each value of time.

We present a method to probe the Out-of-Time-Order Correlators (OTOCs) of a general system by coupling it to a harmonic oscillator probe. When the system's degrees of freedom are traced out, the OTOCs imprint themselves on the generalized influence functional of the oscillator. This generalized influence functional leads to a local effective action for the probe whose couplings encode OTOCs of the system. We study the structural features of this effective action and the constraints on the couplings from microscopic unitarity. We comment on how the OTOCs of the system appear in the OTOCs of the probe., Comment: 14 pages+appendices, minor changes

Bulk quantum fields are often said to contribute to the generalized entropy $\frac{A}{4G_N} +S_{\mathrm{bulk}}$ only at $O(1)$. Nonetheless, in the context of evaporating black holes, $O(1/G_N)$ gradients in $S_{\mathrm{bulk}}$ can arise due to large boosts, introducing a quantum extremal surface far from any classical extremal surface. We examine the effect of such bulk quantum effects on quantum extremal surfaces (QESs) and the resulting entanglement wedge in a simple two-boundary $2d$ bulk system defined by Jackiw-Teitelboim gravity coupled to a 1+1 CFT. Turning on a coupling between one boundary and a further external auxiliary system which functions as a heat sink allows a two-sided otherwise-eternal black hole to evaporate on one side. We find the generalized entropy of the QES to behave as expected from general considerations of unitarity, and in particular that ingoing information disappears from the entanglement wedge after a scambling time $\frac{\beta}{2\pi} \ln \Delta S + O(1)$ in accord with expectations for holographic implementations of the Hayden-Preskill protocol. We also find an interesting QES phase transition at what one might call the Page time for our process., Comment: 49 pages, 9 figures; v3: overview section added

In theories with long-range forces like QED or perturbative gravity, only rates that include emitted soft radiation are non-vanishing. Independently of detector resolution, finite observables can only be obtained after integrating over the IR-component of this radiation. This integration can lead to some loss of quantum coherence. In this note, however, we argue that it should in general not lead to full decoherence. Based on unitarity, we suggest a way to define non-vanishing off-diagonal pieces of the IR-finite density matrix. For this IR-finite density matrix, we estimate the dependence of the loss of quantum coherence, i.e. of its purity, on the scattering kinematics., Comment: 17 pages, 2 figures; v2: matches published version