A cortical potential reflecting cardiac function

Emotional trauma and psychological stress can precipitate cardiac arrhythmia and sudden death through arrhythmogenic effects of efferent sympathetic drive. Patients with preexisting heart disease are particularly at risk. Moreover, generation of proarrhythmic activity patterns within cerebral autonomic centers may be amplified by afferent feedback from a dysfunctional myocardium. An electrocortical potential reflecting afferent cardiac information has been described, reflecting individual differences in interoceptive sensitivity (awareness of one's own heartbeats). To inform our understanding of mechanisms underlying arrhythmogenesis, we extended this approach, identifying electrocortical potentials corresponding to the cortical expression of afferent information about the integrity of myocardial function during stress. We measured changes in cardiac response simultaneously with electroencephalography in patients with established ventricular dysfunction. Experimentally induced mental stress enhanced cardiovascular indices of sympathetic activity (systolic blood pressure, heart rate, ventricular ejection fraction, and skin conductance) across all patients. However, the functional response of the myocardium varied; some patients increased, whereas others decreased, cardiac output during stress. Across patients, heartbeat-evoked potential amplitude at left temporal and lateral frontal electrode locations correlated with stress-induced changes in cardiac output, consistent with an afferent cortical representation of myocardial function during stress. Moreover, the amplitude of the heartbeat-evoked potential in the left temporal region reflected the proarrhythmic status of the heart (inhomogeneity of left ventricular repolarization). These observations delineate a cortical representation of cardiac function predictive of proarrhythmic abnormalities in cardiac repolarization. Our findings highlight the dynamic interaction of heart and brain in stress-induced cardiovascular morbidity

The attractive nonlinear delta-function potential

We solve the continuous one-dimensional Schr\"{o}dinger equation for the case of an inverted {\em nonlinear} delta-function potential located at the origin, obtaining the bound state in closed form as a function of the nonlinear exponent. The bound state probability profile decays exponentially away from the origin, with a profile width that increases monotonically with the nonlinear exponent, becoming an almost completely extended state when this approaches two. At an exponent value of two, the bound state suffers a discontinuous change to a delta-like profile. Further increase of the exponent increases again the width of the probability profile, although the bound state is proven to be stable only for exponents below two. The transmission of plane waves across the nonlinear delta potential increases monotonically with the nonlinearity exponent and is insensitive to the sign of its opacity.Comment: submitted to Am. J. of Phys., sixteen pages, three figure

Delta-Function Potential with a Complex Coupling

We explore the Hamiltonian operator H=-d^2/dx^2 + z \delta(x) where x is real, \delta(x) is the Dirac delta function, and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a (real) spectral singularity at E=-z^2/4. For \Re(z)<0, H has an eigenvalue at E=-z^2/4. For the case that \Re(z)>0, H has a real, positive, continuous spectrum that is free from spectral singularities. For this latter case, we construct an associated biorthonormal system and use it to perform a perturbative calculation of a positive-definite inner product that renders H self-adjoint. This allows us to address the intriguing question of the nonlocal aspects of the equivalent Hermitian Hamiltonian for the system. In particular, we compute the energy expectation values for various Gaussian wave packets to show that the non-Hermiticity effect diminishes rapidly outside an effective interaction region.Comment: Published version, 14 pages, 2 figure

Regularized Green's Function for the Inverse Square Potential

A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the regularized version of the model. The application of Sturm-Liouville theory yields a closed expression for the radial energy Green's function. Finally, the equivalence with a recent path-integral treatment of the same problem is explicitly shown.Comment: 10 pages. The final section was expande

Galilean Lee Model of the Delta Function Potential

The scattering cross section associated with a two dimensional delta function has recently been the object of considerable study. It is shown here that this problem can be put into a field theoretical framework by the construction of an appropriate Galilean covariant theory. The Lee model with a standard Yukawa interaction is shown to provide such a realization. The usual results for delta function scattering are then obtained in the case that a stable particle exists in the scattering channel provided that a certain limit is taken in the relevant parameter space. In the more general case in which no such limit is taken finite corrections to the cross section are obtained which (unlike the pure delta function case) depend on the coupling constant of the model.Comment: 7 pages, latex, no figure