On the fluidity of consonance and dissonance: The influence of musical context

The consonance/dissonance (C/D) level of a triadic chord is not a fixed or absolute value. Rather, it is fluid, since C/D depends both on a chord’s sonic characteristics and on the musical context in which it appears. To test the fluidity of C/D—the extent to which C/D perception is dependent on musical context—4 types of chords (major, minor, augmented, and diminished triads) were presented in isolation (“without musical context”) and as part of a short cadence (IV-V-I, “with musical context”). The C/D level of each chord was judged, as was the overall C/D and pleasantness/unpleasantness (P/U) level of the cadences. When isolated, major triads were considered most consonant, followed by minor and diminished triads, while augmented triads were judged most dissonant. In the context of a musical cadence, this rank order remained the same. However, evaluations of the dissonance of augmented and diminished chords varied depending on each chord’s functional position within the cadence. For instance, diminished triads were relatively consonant when on the subdominant, while augmented triads were relatively dissonant when on the tonic. These findings lend support to the hypotheses that: (a) the degree to which the harmonic function of a chord is familiar, and (b) the degree to which a chord’s stability (and hence also the listener’s expectation) is violated contribute to the perception of C/D

Control of Ultra-cold Inelastic Collisions by Feshbash Resonances and Quasi-One-Dimensional Confinement

Cold inelastic collisions of atoms or molecules are analyzed using very general arguments. In free space, the deactivation rate can be enhanced or suppressed together with the scattering length of the corresponding elastic collision via a Feshbach resonance, and by interference of deactivation of the closed and open channels. In reduced dimensional geometries, the deactivation rate decreases with decreasing collision energy and does not increase with resonant elastic scattering length. This has broad implications; e.g., stabilization of molecules in a strongly confining two-dimensional optical lattice, since collisional decay of the highly vibrationally excited states due to inelastic collisions is suppressed. The relation of our results with those based on the Lieb-Liniger model are addressed.Comment: 5 pages, 1 figur

Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement

The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant, hbar/2, as demonstrated by Heisenberg's thought experiment using a gamma-ray microscope. Here I show that this common assumption is false: a universally valid trade-off relation between the noise and the disturbance has an additional correlation term, which is redundant when the intervention brought by the measurement is independent of the measured object, but which allows the noise-disturbance product much below Planck's constant when the intervention is dependent. A model of measuring interaction with dependent intervention shows that Heisenberg's lower bound for the noise-disturbance product is violated even by a nearly nondisturbing, precise position measuring instrument. An experimental implementation is also proposed to realize the above model in the context of optical quadrature measurement with currently available linear optical devices.Comment: Revtex, 6 page

The Standard Model of Quantum Measurement Theory: History and Applications

The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable-to-be-measured is multiplied with some observable of a probe system. This simple Ansatz has proved extremely fruitful in the development of the foundations of quantum mechanics. While the ensuing type of models has often been argued to be rather artificial, recent advances in quantum optics have demonstrated their prinicpal and practical feasibility. A brief historical review of the standard model together with an outline of its virtues and limitations are presented as an illustration of the mutual inspiration that has always taken place between foundational and experimental research in quantum physics.Comment: 22 pages, to appear in Found. Phys. 199

Simulation results for a low energy nuclear recoil yields measurement in liquid xenon using the MiX detector

Measuring the scintillation and ionization yields of liquid xenon in response to ultra-low energy nuclear recoil events is necessary to increase the sensitivity of liquid xenon experiments to light dark matter. Neutron capture on xenon can be used to produce nuclear recoil events with energies below $0.3$ keV$_\text{NR}$ via the asymmetric emission of $\gamma$ rays during nuclear de-excitation. The feasibility of an ultra-low energy nuclear recoil measurement using neutron capture was investigated for the Michigan Xenon (MiX) detector, a small dual-phase xenon time projection chamber that is optimized for a high scintillation gain. Simulations of the MiX detector, a partial neutron moderator, and a pulsed neutron generator indicate that a population of neutron capture events can be isolated from neutron scattering events. Further, the rate of neutron captures in the MiX detector was optimized by varying the thickness of the partial neutron moderator, neutron pulse width, and neutron pulse frequency.Comment: 7 pages, 5 figures. LIDINE 2022 proceeding

Continuous variable quantum cryptography

We propose a quantum cryptographic scheme in which small phase and amplitude modulations of CW light beams carry the key information. The presence of EPR type correlations provides the quantum protection.Comment: 8 pages, 3 figure

Interpretation for a positive P representation

We show that a "canonical" form of the positive P representation has a simple interpretation as the statistics of four detectors, two of which make redundant position measurements, while the other two simultaneously make redundant momentum measurements. This interpretation allows us to understand the additional degrees of freedom for the canonical positive P representation

Path integrals on a flux cone

This paper considers the Schroedinger propagator on a cone with the conical singularity carrying magnetic flux (``flux cone''). Starting from the operator formalism and then combining techniques of path integration in polar coordinates and in spaces with constraints, the propagator and its path integral representation are derived. "Quantum correction" in the Lagrangian appears naturally and no a priori assumption is made about connectivity of the configuration space.Comment: LaTeX file, 9 page

Time-of-arrival distributions from position-momentum and energy-time joint measurements

The position-momentum quasi-distribution obtained from an Arthurs and Kelly joint measurement model is used to obtain indirectly an ``operational'' time-of-arrival (TOA) distribution following a quantization procedure proposed by Kocha\'nski and W\'odkiewicz [Phys. Rev. A 60, 2689 (1999)]. This TOA distribution is not time covariant. The procedure is generalized by using other phase-space quasi-distributions, and sufficient conditions are provided for time covariance that limit the possible phase-space quasi-distributions essentially to the Wigner function, which, however, provides a non-positive TOA quasi-distribution. These problems are remedied with a different quantization procedure which, on the other hand, does not guarantee normalization. Finally an Arthurs and Kelly measurement model for TOA and energy (valid also for arbitrary conjugate variables when one of the variables is bounded from below) is worked out. The marginal TOA distribution so obtained, a distorted version of Kijowski's distribution, is time covariant, positive, and normalized

Quantum Communication with Correlated Nonclassical States

Nonclassical correlations between the quadrature-phase amplitudes of two spatially separated optical beams are exploited to realize a two-channel quantum communication experiment with a high degree of immunity to interception. For this scheme, either channel alone can have an arbitrarily small signal-to-noise ratio (SNR) for transmission of a coherent ``message''. However, when the transmitted beams are combined properly upon authorized detection, the encoded message can in principle be recovered with the original SNR of the source. An experimental demonstration has achieved a 3.2 dB improvement in SNR over that possible with correlated classical sources. Extensions of the protocol to improve its security against eavesdropping are discussed.Comment: 8 pages and 4 figures (Figure 1; Figures 2a, 2b; Figure 2