1. Faucet for wave transmission through rotation of waveguide
Artem Pilipchuk and Alina Lyapina
Kirensky Institute of Physics, Federal Research
Center KSC SB RAS, Krasnoyarsk, Russia

2. Philosophical Transactions of the Royal Society of London
Thomas Young speaking on 24 November 1803, to the Royal Society of London, began his description of the historic experiment on double-slit interference. His talk was published in the following year's Philosophical Transactions, and was destined to become a classic, still reprinted and read today.
The Bakerian Lecture: Experiments and Calculations Relative to Physical Optics
Thomas Young
Philosophical Transactions of the Royal Society of London
Vol. 94 (1804), pp. 1-16

3. Milestones of wave interference (by chronology)
1. J. von Neumann and E. Wigner, Z. Phys (1929)
Bound states in the continuum (BSC)
H. Friedrich and D. Wintgen, "Interferring resonances and bound states in the continuum,“ PRA (1985).
Phys. Rev. (1959)

4. 3. Fano asymmetric resonance

5. 4. Topological singularities or vortices

6. Rotation of waveguide unites
all these phase features

7. Effective non-Hermitian Hamiltonian
U.Fano, Phys. Rev. 124, 1866 (1961).
H. Feshbach, Ann. Phys. (New York) (1958) ; (1962) .
C. Mahaux, H.A. Weidenmuller, Shell-Model Approach to Nuclear Reactions, North-Holland, Amsterdam, 1969.
I.Rotter, Rep. Prog. Phys., 54, 635 (1991).
H.-J. Stockmann and Petr Seba, JPA (1998).
H.-J. Stockmann, Quantum Chaos (1999).
K. Pichugin, H. Schanz, and Petr Seba, Phys. Rev. E (2001).
Sadreev and I. Rotter, JPA (2002).
W is matrix NxM where N is the number of eigen states of closed quantum
system, M is the number of continua (channels)

8. Albeverio, Kurasov, Kus, and Petr Seba, J.Math. Phys. (1966):
Fyodorov and Sommers, J. Math. Phys. 38, 1918 (1997)
Pichugin, Schanz, and Petr Seba, Phys. Rev. E (2001).

9. How to tune transmission spectra (Fano resonances) ?
1. Change of eigenvalues

10. 2. Vary the coupling strength
S. Rotter, F. Libisch, J. Burgoffer, U. Kuhl, and H.-J. Stockmann,
"Tunable Fano resonances in transport through microwave billiards“, PRE (2004).

11. 3. Make the coupling strengths complex by rotation of waveguidez
The continua of waveguides
The Neumann BC
Resonator

12. Effective non-Hermitian Hamiltonian

13. Phase transformation of continua

14. Transmittance in the first channel p=0, q=1

16. Wave faucet

17. Sadreev and I. Rotter, JPA (2003)
I.Rotter, Rep. Prog. Phys., 54, 635 (1991)
Okolowicz, Ploszajczak, and I. Rotter, Phys. Rep. (2003)
Sadreev and I. Rotter, JPA (2003)

18. Numerous events of zero resonant widths, bound states in the continuum
Symmetry protected BSCs

19. BSC 1

20. Coupling with evanescent modes of channels p=+/- 1,q=1
Coupling with propagating
modes of the channel p=0, q=1

21. Hermitian
anti-Hermitian
Shifted waveguides lift
a degeneracy of cylindrical
Resonator relative to +\- m

22. It is easy to find the symmetry protected

23. Bound state in the continuums due to interference of states 211, -211, 112, and -112BS

24. Twisted BSCs

25. No spinning currents because evanescent modes of shifted
Spinning bound states in the continuum
R. Parker, "Acoustic resonances and blade vibration in axial
flow compressors", J. Sound and Vibration (1984).
Y. Duan and M. McIver, "Rotational acoustic resonances in
cylindrical waveguides", Wave Motion (2004).
No spinning currents because evanescent modes of shifted
waveguides lift a degeneracy +\- m
Phase of the scattering function
at z=L/2

27. Eigenlevel 012 crosses eigenlevel +-2 11

28. conclusions
Rotation of input or output waveguide in respect to resonator attributes
phase factors into the coupling matrix elements
2. That in turn strongly effects Fano resonances and respectively wave transmittance.
Wave faucet.
3. There is discrete set of the rotation angles at which wave localizes inside the resonator,
bound states in the continuum of both waveguides, left and rotated right ones.
Trapping of sound waves. Collapse of Fano resonance, when unit transmittance coalesces
with zero transmittance.
4. Evanesvcent modes of rotated waveguide gives rise to modification of
Hamiltonian of cylindrical resonator whose eigenvalues dependent on the
rotation angle and lift the degeneracy relative to the azimuthal quantum number.
Analogue with magnetic flux.