Department of Mathematics
University of Virginia
Charlottesville, VA 22903                                                                                           
Office: 228 Kerchof Hall                                                                                                                                               
Phone: 434-924-4933
FAX: 434-982-3084


Office hours:
Monday:  2:00-3:00pm; Wednesday:  4:00-5:00pm



Ira Herbst
     Ph.D., Physics, University of California-Berkeley, 1971




Most of my work is in quantum mechanics and covers a range of subjects from non-relativistic quantum electrodynamics to quantum resonance problems with electric fields. My objective has been to choose problems with some relation to physics, but with the overriding factor to make sure that the mathematical content is interesting and challenging.

Selected papers:

1.     H. Cornean, I. Herbst and G. Nenciu, On the construction of composite Wannier functions, Ann. Henri Poincare’ 17 (2016), 3361-3398. (arXiv:1506.07435)

2.     I. Herbst and J. Rama, Instability of pre-existing resonances under a small constant electric field, Ann. Henri Poincare’ 16 (2015), 2783-2835. AHP Prize Paper (arXiv: 1310.4745)

3.     I. Herbst and R. Mavi, Can we trust the relationship between resonance poles and lifetimes?, J. Phys. A: Math. Theor. 49 (Institute of Physics Select Paper). (arXiv: 1511.03724)

4.     I. Herbst and E. Skibsted, Decay of eigenfunctions of elliptic PDE's., Adv. Math. 270 (2014), 138-180. (arXiv:1306.6878)

5.      I. Herbst and E. Skibsted, decay of eigenfunctions of elliptic PDE’s,II, Adv. Math. 306 (2017) 177-199. (arXiv: 1504.07128)

6.     D. Hasler and I. Herbst, Ground states in the spin boson model, Ann. Henri Poincaré 12 (2011), 621-677. AHP Distinguished Paper Award (arXiv: 1003.5923)

7.     I. Herbst and E. Skibsted: Analyticity estimates for the Navier-Stokes equations, Adv. Math.} 228 (2011), 1990--2033. (arXiv:math-ph/0907.4351)

8.     D. Hasler and I. Herbst: Absence of ground states for a class of translation invariant models of non-relativistic QED, Comm. Math. Phys. 279 (2008), no. 3, 769--787. (arXiv:/0702096)

9.     H. Cornean, I. Herbst, and E. Skibsted: Spiraling attractors and quantum dynamics for a class of long-range magnetic fields, J. Funct. Anal. 247(2007), no. 1, 1-94. [ARTICLE IN PDF]

10.  I. Herbst and E. Skibsted: Absence of quantum states corresponding to unstable classical channels, Ann. Henri Poincaré 9 (2008), 509-552. (arXiv:0710.0594)

11.  I. Herbst and E. Skibsted: Quantum scattering for potentials independent of |x|: Asymptotic completeness for high and low energies, Comm. Partial Differential Equations 29 (2004), no. 3-4, 547-610. [ARTICLE IN PDF]

12.  R. Froese and I. Herbst: Realizing holonomic constraints in classical and quantum mechanics, Comm. Math. Phys. 220 (2001) 489-535. [ARTICLE IN PDF]

13.  S. Agmon, I. Herbst, and E. Skibsted: Perturbation of embedded eigenvalues in the generalized N-body problem, Comm. Math. Phys. 122 (1989), no. 3, 411-438. [ARTICLE IN PDF]

14.  R. Froese and I. Herbst: Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators, Comm. Math. Phys. 87 (1982/83), no. 3, 429-447. [ARTICLE IN PDF]

15.  I. Herbst and B. Simon: Dilation analyticity in constant electric field, II: N-body problem, Borel summability, Comm. Math. Phys. 80 (1981) 181-216.